ALEKS 360 ACCESS CARD PRECALCULUS 18 WK
1st Edition
ISBN: 9781265748456
Author: Miller
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 4.1, Problem 111PE
The Earth's orbit around the Sun is elliptical (oval shaped). However, the elongation is small, and for our discussion here, we take the orbit to be circular with a radius of approximately
a. Find the linear speed (in mph) of the Earth through its orbit around the Sun. Round to the nearest hundred miles per hour.
b. How far does the Earth travel in its orbit in one day? Round to the nearest thousand miles.
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Students have asked these similar questions
A ladder 25 feet long is leaning against the wall of a building. Initially, the foot of the ladder is 7 feet from the wall. The foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. The location of the foot of the ladder, its x coordinate, at time t seconds is given by
x(t)=7+2t.
wall
y(1)
25 ft. ladder
x(1)
ground
(a) Find the formula for the location of the top of the ladder, the y coordinate, as a function of time t. The formula for y(t)= √ 25² - (7+2t)²
(b) The domain of t values for y(t) ranges from 0
(c) Calculate the average velocity of the top of the ladder on each of these time intervals (correct to three decimal places):
. (Put your cursor in the box, click and a palette will come up to help you enter your symbolic answer.)
time interval
ave velocity
[0,2]
-0.766
[6,8]
-3.225
time interval
ave velocity
-1.224
-9.798
[2,4]
[8,9]
(d) Find a time interval [a,9] so that the average velocity of the top of the ladder on this…
Total marks 15
3.
(i)
Let FRN Rm be a mapping and x = RN is a given
point. Which of the following statements are true? Construct counterex-
amples for any that are false.
(a)
If F is continuous at x then F is differentiable at x.
(b)
If F is differentiable at x then F is continuous at x.
If F is differentiable at x then F has all 1st order partial
(c)
derivatives at x.
(d) If all 1st order partial derivatives of F exist and are con-
tinuous on RN then F is differentiable at x.
[5 Marks]
(ii) Let mappings
F= (F1, F2) R³ → R² and
G=(G1, G2) R² → R²
:
be defined by
F₁ (x1, x2, x3) = x1 + x²,
G1(1, 2) = 31,
F2(x1, x2, x3) = x² + x3,
G2(1, 2)=sin(1+ y2).
By using the chain rule, calculate the Jacobian matrix of the mapping
GoF R3 R²,
i.e., JGoF(x1, x2, x3). What is JGOF(0, 0, 0)?
(iii)
[7 Marks]
Give reasons why the mapping Go F is differentiable at
(0, 0, 0) R³ and determine the derivative matrix D(GF)(0, 0, 0).
[3 Marks]
5.
(i)
Let f R2 R be defined by
f(x1, x2) = x² - 4x1x2 + 2x3.
Find all local minima of f on R².
(ii)
[10 Marks]
Give an example of a function f: R2 R which is not bounded
above and has exactly one critical point, which is a minimum. Justify briefly
Total marks 15
your answer.
[5 Marks]
Chapter 4 Solutions
ALEKS 360 ACCESS CARD PRECALCULUS 18 WK
Ch. 4.1 - Convert 1311233 to decimal degrees. Round to 4...Ch. 4.1 - Convert 26.48 to degree, minute, second form.Ch. 4.1 - Convert from degrees to radians. a. 300 b. 70Ch. 4.1 - Convert from radians to degrees. a. 18 b. 74Ch. 4.1 - Find an angle coterminal to between 0 and 360 ....Ch. 4.1 - Find an angle coterminal to on the interval [0,2)...Ch. 4.1 - Find the length of the arc made by an angle of 220...Ch. 4.1 - Lincoln, Nebraska, is located at 40.8N,96.7W and...Ch. 4.1 - A bicycle wheel rotates at 2 revolutions per...Ch. 4.1 - A sprinkler rotates through an angle of 120 and...
Ch. 4.1 - Prob. 1PECh. 4.1 - An angle with its vertex at the origin of an...Ch. 4.1 - Two common units used to measure angles are and .Ch. 4.1 - One degree is what fractional amount of a full...Ch. 4.1 - An angle that measures 360 has a measure of ...Ch. 4.1 - Two angles are called if the sum of their...Ch. 4.1 - An angle with measure or radians is a right...Ch. 4.1 - A(n) angle has a measure between 0 and 90 ....Ch. 4.1 - One degree is equally divided into 60 parts called...Ch. 4.1 - One minute is equally divided into 60 parts called...Ch. 4.1 - 1='='Ch. 4.1 - An angle with its vertex at the center of a circle...Ch. 4.1 - A central angle of a circle that intercepts an arc...Ch. 4.1 - Which angle has a greater measure, 2 or 2 radians?Ch. 4.1 - To convert from radians to degrees, multiply by ...Ch. 4.1 - Two angles are if they have the same initial side...Ch. 4.1 - The measure of all angles coterminal to 74 differ...Ch. 4.1 - The measure of all angles coterminal to 112 differ...Ch. 4.1 - The length s of an arc made by an angle on a...Ch. 4.1 - To locate points on the surface of the Earth that...Ch. 4.1 - The relationship v=arclengthtime represents the ...Ch. 4.1 - The symbol is typically used to denote speed and...Ch. 4.1 - A wedge of a circle, similar in shape to a slice...Ch. 4.1 - The area A of a sector of a circle of radius r...Ch. 4.1 - For Exercises 25-26, sketch the angles in standard...Ch. 4.1 - For Exercises 25-26, sketch the angles in standard...Ch. 4.1 - For Exercises 27-30, convert the given angle to...Ch. 4.1 - For Exercises 27-30, convert the given angle to...Ch. 4.1 - For Exercises 27-30, convert the given angle to...Ch. 4.1 - For Exercises 27-30, convert the given angle to...Ch. 4.1 - For Exercises 31-34, convert the given angle to...Ch. 4.1 - For Exercises 31-34, convert the given angle to...Ch. 4.1 - For Exercises 31-34, convert the given angle to...Ch. 4.1 - For Exercises 31-34, convert the given angle to...Ch. 4.1 - Prob. 35PECh. 4.1 - Prob. 36PECh. 4.1 - For Exercises 37-40, convert from degrees to...Ch. 4.1 - Prob. 38PECh. 4.1 - Prob. 39PECh. 4.1 - For Exercises 37-40, convert from degrees to...Ch. 4.1 - Prob. 41PECh. 4.1 - Prob. 42PECh. 4.1 - For Exercises 41-44, convert from degrees to...Ch. 4.1 - For Exercises 41-44, convert from degrees to...Ch. 4.1 - For Exercises 45-56, convert from radians to...Ch. 4.1 - For Exercises 45-56, convert from radians to...Ch. 4.1 - Prob. 47PECh. 4.1 - For Exercises 45-56, convert from radians to...Ch. 4.1 - Prob. 49PECh. 4.1 - Prob. 50PECh. 4.1 - For Exercises 45-56, convert from radians to...Ch. 4.1 - Prob. 52PECh. 4.1 - Prob. 53PECh. 4.1 - For Exercises 45-56, convert from radians to...Ch. 4.1 - For Exercises 45-56, convert from radians to...Ch. 4.1 - For Exercises 45-56, convert from radians to...Ch. 4.1 - Prob. 57PECh. 4.1 - For Exercises 57-64, find a positive angle and a...Ch. 4.1 - For Exercises 57-64, find a positive angle and a...Ch. 4.1 - For Exercises 57-64, find a positive angle and a...Ch. 4.1 - For Exercises 57-64, find a positive angle and a...Ch. 4.1 - For Exercises 57-64, find a positive angle and a...Ch. 4.1 - Prob. 63PECh. 4.1 - For Exercises 57-64, find a positive angle and a...Ch. 4.1 - For Exercises 65-70, find an angle between 0 and...Ch. 4.1 - For Exercises 65-70, find an angle between 0 and...Ch. 4.1 - For Exercises 65-70, find an angle between 0 and...Ch. 4.1 - For Exercises 65-70, find an angle between 0 and...Ch. 4.1 - For Exercises 65-70, find an angle between 0 and...Ch. 4.1 - For Exercises 65-70, find an angle between 0 and...Ch. 4.1 - Prob. 71PECh. 4.1 - For Exercises 71-74, find the exact length of the...Ch. 4.1 - Prob. 73PECh. 4.1 - For Exercises 71-74, find the exact length of the...Ch. 4.1 - A 6-ft pendulum swings through an angle of 4036 ....Ch. 4.1 - A gear with a 1.2-cm radius moves through an angle...Ch. 4.1 - a. What is the geographical relationship between...Ch. 4.1 - For Exercises 79-82, assume that the Earth is...Ch. 4.1 - For Exercises 79-82, assume that the Earth is...Ch. 4.1 - For Exercises 79-82, assume that the Earth is...Ch. 4.1 - For Exercises 79-82, assume that the Earth is...Ch. 4.1 - A pulley is 16cm in diameter. a. Find the distance...Ch. 4.1 - A pulley is 1.2ft. in diameter. a. Find the...Ch. 4.1 - A hoist is used to lift a palette of bricks. The...Ch. 4.1 - A winch on a sailboat is 8in. in diameter and is...Ch. 4.1 - A surveyor uses a subtense bar to find the...Ch. 4.1 - A surveyor uses a subtense bar to find the...Ch. 4.1 - A circular paddle wheel of radius 3ft is lowered...Ch. 4.1 - An energy-efficient hard drive has a 2.5-in ....Ch. 4.1 - A 714-in.-diameter circular saw has 24 teeth and...Ch. 4.1 - On a weed-cutting device, a thick nylon line...Ch. 4.1 - A truck has 2.5-ft tires (in diameter). a. What...Ch. 4.1 - A bicycle has 25-in . wheels (in diameter). a....Ch. 4.1 - Prob. 95PECh. 4.1 - For Exercises 95-98, find the exact area of the...Ch. 4.1 - Prob. 97PECh. 4.1 - For Exercises 95-98, find the exact area of the...Ch. 4.1 - A slice of a circular pizza 12in .in diameter is...Ch. 4.1 - A circular cheesecake 9in. in diameter is cut into...Ch. 4.1 - The back wiper blade on an SUV extends 3in. from...Ch. 4.1 - A robotic arm rotates through an angle of 160 . It...Ch. 4.1 - Prob. 103PECh. 4.1 - Prob. 104PECh. 4.1 - Prob. 105PECh. 4.1 - Prob. 106PECh. 4.1 - Prob. 107PECh. 4.1 - Prob. 108PECh. 4.1 - The second hand of a clock moves from 12:10 to...Ch. 4.1 - The minute hand of a clock moves from 12:10 to...Ch. 4.1 - The Earth's orbit around the Sun is elliptical...Ch. 4.1 - The Earth completes one full rotation around its...Ch. 4.1 - Two gears are calibrated so that the smaller gear...Ch. 4.1 - Two gears are calibrated so that the larger gear...Ch. 4.1 - A spinning-disc confocal microscope contains a...Ch. 4.1 - For Exercises 116-119, approximate the area of the...Ch. 4.1 - For Exercises 116-119, approximate the area of the...Ch. 4.1 - For Exercises 116-119, approximate the area of the...Ch. 4.1 - For Exercises 116-119, approximate the area of the...Ch. 4.1 - Explain what is meant by 1 radian. Explain what is...Ch. 4.1 - For an angle drawn in standard position, explain...Ch. 4.1 - As the fan rotates (see figure), which point A or...Ch. 4.1 - If an angle of a sector is held constant, but the...Ch. 4.1 - If an angle of a sector is doubled, but the radius...Ch. 4.1 - When a person pedals a bicycle, the front sprocket...Ch. 4.1 - In the third century B.C. , the Greek astronomer...Ch. 4.1 - The space shuttle program involved 135 manned...Ch. 4.1 - Prob. 128PECh. 4.1 - Prob. 129PECh. 4.1 - Prob. 130PECh. 4.1 - Prob. 131PECh. 4.1 - Prob. 132PECh. 4.1 - Prob. 133PECh. 4.1 - Prob. 134PECh. 4.2 - Suppose that the real number t corresponds to the...Ch. 4.2 - Prob. 2SPCh. 4.2 - Prob. 3SPCh. 4.2 - Given sint=37 and cost=2107 use the reciprocal and...Ch. 4.2 - Prob. 5SPCh. 4.2 - Prob. 6SPCh. 4.2 - Prob. 7SPCh. 4.2 - Use the properties of the trigonometric functions...Ch. 4.2 - Use a calculator to approximate the function...Ch. 4.2 - The graph of x2+y2=1 is known as the circle. It...Ch. 4.2 - The circumference of the unit circle is . Thus,...Ch. 4.2 - Prob. 3PECh. 4.2 - Prob. 4PECh. 4.2 - Prob. 5PECh. 4.2 - The domain of the trigonometric functions and is...Ch. 4.2 - Prob. 7PECh. 4.2 - Prob. 8PECh. 4.2 - The period of the tangent and cotangent functions...Ch. 4.2 - The cosine function is an function because...Ch. 4.2 - For Exercises 11-14, determine if the point lies...Ch. 4.2 - Prob. 12PECh. 4.2 - Prob. 13PECh. 4.2 - For Exercises 11-14, determine if the point lies...Ch. 4.2 - For Exercises 15-18, the real number t corresponds...Ch. 4.2 - For Exercises 15-18, the real number t corresponds...Ch. 4.2 - Prob. 17PECh. 4.2 - Prob. 18PECh. 4.2 - Prob. 19PECh. 4.2 - Prob. 20PECh. 4.2 - For Exercises 20-23, identify the coordinates of...Ch. 4.2 - For Exercises 20-23, identify the coordinates of...Ch. 4.2 - Prob. 23PECh. 4.2 - For Exercises 24-26, identify the ordered pairs on...Ch. 4.2 - Prob. 25PECh. 4.2 - For Exercises 24-26, identify the ordered pairs on...Ch. 4.2 - For Exercises 27-32, evaluate the trigonometric...Ch. 4.2 - For Exercises 27-32, evaluate the trigonometric...Ch. 4.2 - For Exercises 27-32, evaluate the trigonometric...Ch. 4.2 - For Exercises 27-32, evaluate the trigonometric...Ch. 4.2 - For Exercises 27-32, evaluate the trigonometric...Ch. 4.2 - For Exercises 27-32, evaluate the trigonometric...Ch. 4.2 - For Exercises 33-38, select the domain of the...Ch. 4.2 - Prob. 34PECh. 4.2 - For Exercises 33-38, select the domain of the...Ch. 4.2 - For Exercises 33-38, select the domain of the...Ch. 4.2 - Prob. 37PECh. 4.2 - Prob. 38PECh. 4.2 - For Exercises 39-42, evaluate the function if...Ch. 4.2 - For Exercises 39-42, evaluate the function if...Ch. 4.2 - For Exercises 39-42, evaluate the function if...Ch. 4.2 - For Exercises 39-42, evaluate the function if...Ch. 4.2 - For Exercises 43-46, given the values for sint and...Ch. 4.2 - For Exercises 43-46, given the values for sint and...Ch. 4.2 - Prob. 45PECh. 4.2 - For Exercises 43-46, given the values for sint and...Ch. 4.2 - For Exercises 47-48, derive the given identity...Ch. 4.2 - Prob. 48PECh. 4.2 - For Exercises 49-54, use an appropriate...Ch. 4.2 - For Exercises 49-54, use an appropriate...Ch. 4.2 - For Exercises 49-54, use an appropriate...Ch. 4.2 - For Exercises 49-54, use an appropriate...Ch. 4.2 - Prob. 53PECh. 4.2 - Prob. 54PECh. 4.2 - Write sin t in terms of cos t for a. t in Quadrant...Ch. 4.2 - Prob. 56PECh. 4.2 - Write cott in terms of csct for a. t in Quadrant...Ch. 4.2 - Write cost in terms of sint for a. t in Quadrant...Ch. 4.2 - Given that cos2912=624 determine the value of...Ch. 4.2 - Given that sec1112=26 , determine the value of...Ch. 4.2 - Prob. 61PECh. 4.2 - Given that sin10=514 , determine the value of...Ch. 4.2 - For Exercises 63-66, use the periodic properties...Ch. 4.2 - For Exercises 63-66, use the periodic properties...Ch. 4.2 - Prob. 65PECh. 4.2 - Prob. 66PECh. 4.2 - For Exercises 67-74, use the even-odd and periodic...Ch. 4.2 - Prob. 68PECh. 4.2 - For Exercises 67-74, use the even-odd and periodic...Ch. 4.2 - For Exercises 67-74, use the even odd and periodic...Ch. 4.2 - Prob. 71PECh. 4.2 - For Exercises 67-74, use the even-odd and periodic...Ch. 4.2 - For Exercises 67-74, use the even-odd and periodic...Ch. 4.2 - For Exercises 67-74, use the even-odd and periodic...Ch. 4.2 - Use a calculator to approximate the function...Ch. 4.2 - Use a calculator to approximate the function...Ch. 4.2 - Use a calculator to approximate the function...Ch. 4.2 - Use a calculator to approximate the function...Ch. 4.2 - For Exercises 79-80 evaluate sint, cost, and tant...Ch. 4.2 - Prob. 80PECh. 4.2 - Prob. 81PECh. 4.2 - For Exercises 81-86, identify the values of t on...Ch. 4.2 - For Exercises 81-86, identify the values of t on...Ch. 4.2 - Prob. 84PECh. 4.2 - For Exercises 81-86, identify the values of t on...Ch. 4.2 - For Exercises 81-86, identify the values of t on...Ch. 4.2 - For Exercises 87-92, select all properties that...Ch. 4.2 - For Exercises 87-92, select all properties that...Ch. 4.2 - For Exercises 87-92, select all properties that...Ch. 4.2 - For Exercises 87-92, select all properties that...Ch. 4.2 - For Exercises 87-92, select all properties that...Ch. 4.2 - For Exercises 87-92, select all properties that...Ch. 4.2 - Prob. 93PECh. 4.2 - Prob. 94PECh. 4.2 - Prob. 95PECh. 4.2 - For exercises 93-98, simplify using properties of...Ch. 4.2 - Prob. 97PECh. 4.2 - For exercises 93-98, simplify using properties of...Ch. 4.2 - Prob. 99PECh. 4.2 - The fluctuating brightness of a distant star is...Ch. 4.2 - Prob. 101PECh. 4.2 - For exercises 101-104, identify each function as...Ch. 4.2 - Prob. 103PECh. 4.2 - For exercises 101-104, identify each function as...Ch. 4.2 - Describe the changes in sint and cost as t...Ch. 4.2 - Prob. 106PECh. 4.2 - Explain why 1cost1 and 1sint1 for all real numbers...Ch. 4.2 - Prob. 108PECh. 4.2 - For Exercises 109-114, use the figure to estimate...Ch. 4.2 - Prob. 110PECh. 4.2 - Prob. 111PECh. 4.2 - For Exercises 109-114, use the figure to estimate...Ch. 4.2 - Prob. 113PECh. 4.2 - Prob. 114PECh. 4.2 - For Exercises 115-120, use the figure from...Ch. 4.2 - Prob. 116PECh. 4.2 - Prob. 117PECh. 4.2 - For Exercises 115-120, use the figure from...Ch. 4.2 - Prob. 119PECh. 4.2 - Prob. 120PECh. 4.2 - Prob. 121PECh. 4.2 - Prove that the period of ft=cost is 2 .Ch. 4.2 - Prob. 123PECh. 4.2 - Consider the expression 1cost1 a. What is the...Ch. 4.3 - Prob. 1SPCh. 4.3 - Prob. 2SPCh. 4.3 - Prob. 3SPCh. 4.3 - Evaluate sin30 , cos30 , and tan30 .Ch. 4.3 - Simplify the expressions. a. cot60cot30 b....Ch. 4.3 - For each function value, find a cofunction with...Ch. 4.3 - Suppose that a farm worker determines that the...Ch. 4.3 - If a 15-ft ladder is leaning against a wall at an...Ch. 4.3 - In a right triangle with an acute angle the...Ch. 4.3 - The leg of a right triangle that lies on one ray...Ch. 4.3 - The mnemonic device "SOH-CAH-TOA" stands for the...Ch. 4.3 - Complete the reciprocal and quotient identities,...Ch. 4.3 - Given the lengths of two sides of a right...Ch. 4.3 - An right triangle is a right triangle in which...Ch. 4.3 - The length of the shorter leg of a 306090 triangle...Ch. 4.3 - For the six trigonometric functions...Ch. 4.3 - tan is the of sin and cos .Ch. 4.3 - Complete the Pythagorean identities....Ch. 4.3 - The two acute angles in a right triangle are...Ch. 4.3 - The sine of angle equals the cosine of . For this...Ch. 4.3 - For Exercises 13-14, find the exact values of the...Ch. 4.3 - For Exercises 13-14, find the exact values of the...Ch. 4.3 - For Exercises 15-18, first use the Pythagorean...Ch. 4.3 - For Exercises 15-18, first use the Pythagorean...Ch. 4.3 - Prob. 17PECh. 4.3 - For Exercises 15-18, first use the Pythagorean...Ch. 4.3 - For Exercises 19-22, first use the Pythagorean...Ch. 4.3 - For Exercises 19-22, first use the Pythagorean...Ch. 4.3 - Prob. 21PECh. 4.3 - Prob. 22PECh. 4.3 - In Exercises 23-24, given the value of one...Ch. 4.3 - In Exercises 23-24, given the value of one...Ch. 4.3 - For Exercises 25-30, assume that is an acute...Ch. 4.3 - For Exercises 25-30, assume that is an acute...Ch. 4.3 - Prob. 27PECh. 4.3 - For Exercises 25-30, assume that is an acute...Ch. 4.3 - Prob. 29PECh. 4.3 - For Exercises 25-30, assume that is an acute...Ch. 4.3 - Prob. 31PECh. 4.3 - a. Evaluate sin60 . b. Evaluate sin30+sin30 . c....Ch. 4.3 - For Exercises 33-38, find the exact value of each...Ch. 4.3 - For Exercises 33-38, find the exact value of each...Ch. 4.3 - Prob. 35PECh. 4.3 - For Exercises 33-38, find the exact value of each...Ch. 4.3 - For Exercises 33-38, find the exact value of each...Ch. 4.3 - For Exercises 33-38, find the exact value of each...Ch. 4.3 - Prob. 39PECh. 4.3 - Prob. 40PECh. 4.3 - For Exercises 39-44, determine whether the...Ch. 4.3 - Prob. 42PECh. 4.3 - Prob. 43PECh. 4.3 - For Exercises 39-44, determine whether the...Ch. 4.3 - For Exercises 45-50, given the function value,...Ch. 4.3 - For Exercises 45-50, given the function value,...Ch. 4.3 - Prob. 47PECh. 4.3 - For Exercises 45-50, given the function value,...Ch. 4.3 - For Exercises 45-50, given the function value,...Ch. 4.3 - For Exercises 45-50, given the function value,...Ch. 4.3 - For Exercises 51-54, use a calculator to...Ch. 4.3 - For Exercises 51-54, use a calculator to...Ch. 4.3 - For Exercises 51-54, use a calculator to...Ch. 4.3 - For Exercises 51-54, use a calculator to...Ch. 4.3 - An observer at the top of a 426-ft cliff measures...Ch. 4.3 - A lamppost casts a shadow of 18ft when the angle...Ch. 4.3 - A 30-ft boat ramp makes a 7 angle with the water....Ch. 4.3 - Prob. 58PECh. 4.3 - The Lookout Mountain Incline Railway, located in...Ch. 4.3 - A 12-ft ladder learning against a house makes a 64...Ch. 4.3 - According to National Football League (NFL) rules,...Ch. 4.3 - A zip line is to be built between two towers...Ch. 4.3 - To determine the width of a river from point A to...Ch. 4.3 - For Exercises 64-68, use the fundamental...Ch. 4.3 - For Exercises 64-68, use the fundamental...Ch. 4.3 - For Exercises 64-68, use the fundamental...Ch. 4.3 - For Exercises 64-68, use the fundamental...Ch. 4.3 - Prob. 68PECh. 4.3 - Prob. 69PECh. 4.3 - An airplane traveling 400 mph at a cruising...Ch. 4.3 - A scientist standing at the top of a mountain 2mi...Ch. 4.3 - Prob. 72PECh. 4.3 - Find the exact lengths x,y , and z .Ch. 4.3 - Use the figure to explain why tan=cot90 .Ch. 4.3 - Prob. 75PECh. 4.3 - An athlete is in a boat at point A, 14mi from the...Ch. 4.3 - Prob. 77PECh. 4.3 - In the figure, CD=15,DE=8,tan=43 and sin=35 , Find...Ch. 4.3 - Prob. 79PECh. 4.3 - Prob. 80PECh. 4.3 - Use a cofunction relationship to show that the...Ch. 4.3 - For Exercises 82-85, use a calculator to...Ch. 4.3 - For Exercises 82-85, use a calculator to...Ch. 4.3 - Prob. 84PECh. 4.3 - For Exercises 82-85, use a calculator to...Ch. 4.4 - Let p5,7 be a point on the terminal side of angle ...Ch. 4.4 - Find the reference angle . a. =150 b. =157.5 c....Ch. 4.4 - Evaluate the functions. a. cos56 b. cot120 c....Ch. 4.4 - Evaluate the functions. a. csc11 b. cos600Ch. 4.4 - Given cos=38 and sin0 , find and tan .Ch. 4.4 - Given sin=513 for in Quadrant IV, find cos , and...Ch. 4.4 - The distance from the origin to a point Px,y is...Ch. 4.4 - Prob. 2PECh. 4.4 - If is an angle in standard position, the angle...Ch. 4.4 - The values tan and sec are undefined for odd...Ch. 4.4 - The values cot and csc are undefined for multiples...Ch. 4.4 - For what values of is sin greater than 1 ?Ch. 4.4 - Let px,y be a point on the terminal side of an...Ch. 4.4 - Fill in the cells in the table with the...Ch. 4.4 - For Exercises 9-14, given the stated conditions,...Ch. 4.4 - For Exercises 9-14, given the stated conditions,...Ch. 4.4 - Prob. 11PECh. 4.4 - For Exercises 9-14, given the stated conditions,...Ch. 4.4 - For Exercises 9-14, given the stated conditions,...Ch. 4.4 - For Exercises 9-14, given the stated conditions,...Ch. 4.4 - Prob. 15PECh. 4.4 - For Exercises 15-20, a point is given on the...Ch. 4.4 - For Exercises 15-20, a point is given on the...Ch. 4.4 - For Exercises 15-20, a point is given on the...Ch. 4.4 - For Exercises 15-20, a point is given on the...Ch. 4.4 - For Exercises 15-20, a point is given on the...Ch. 4.4 - Complete the table for the given angles.Ch. 4.4 - Prob. 22PECh. 4.4 - For Exercises 23-30, find the reference angle for...Ch. 4.4 - For Exercises 23-30, find the reference angle for...Ch. 4.4 - For Exercises 23-30, find the reference angle for...Ch. 4.4 - For Exercises 23-30, find the reference angle for...Ch. 4.4 - For Exercises 23-30, find the reference angle for...Ch. 4.4 - Prob. 28PECh. 4.4 - For Exercises 23-30, find the reference angle for...Ch. 4.4 - For Exercises 23-30, find the reference angle for...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - Prob. 33PECh. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - Prob. 45PECh. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - Prob. 50PECh. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - Prob. 53PECh. 4.4 - For Exercises 31-54, use reference angles to find...Ch. 4.4 - For Exercises 55-58, find two angles between 0 and...Ch. 4.4 - For Exercises 55-58, find two angles between 0 and...Ch. 4.4 - For Exercises 55-58, find two angles between 0 and...Ch. 4.4 - Prob. 58PECh. 4.4 - For Exercises 59-62, find two angles between 0 and...Ch. 4.4 - Prob. 60PECh. 4.4 - For Exercises 59-62, find two angles between 0 and...Ch. 4.4 - For Exercises 59-62, find two angles between 0 and...Ch. 4.4 - In Exercises 63-68, find the values of the...Ch. 4.4 - In Exercises 63-68, find the values of the...Ch. 4.4 - In Exercises 63-68, find the values of the...Ch. 4.4 - In Exercises 63-68, find the values of the...Ch. 4.4 - In Exercises 63-68, find the values of the...Ch. 4.4 - In Exercises 63-68, find the values of the...Ch. 4.4 - Prob. 69PECh. 4.4 - For Exercises 69-74, use fundamental trigonometric...Ch. 4.4 - For Exercises 69-74, use fundamental trigonometric...Ch. 4.4 - For Exercises 69-74, use fundamental trigonometric...Ch. 4.4 - Prob. 73PECh. 4.4 - For Exercises 69-74, use fundamental trigonometric...Ch. 4.4 - Prob. 75PECh. 4.4 - For Exercises 75-76, find the sign of the...Ch. 4.4 - For Exercises 77-84, suppose that is an acute...Ch. 4.4 - For Exercises 77-84, suppose that is an acute...Ch. 4.4 - For Exercises 77-84, suppose that is an acute...Ch. 4.4 - For Exercises 77-84, suppose that is an acute...Ch. 4.4 - For Exercises 77-84, suppose that is an acute...Ch. 4.4 - Prob. 82PECh. 4.4 - Prob. 83PECh. 4.4 - For Exercises 77-84, suppose that is an acute...Ch. 4.4 - For Exercises 85-90, find the value of each...Ch. 4.4 - For Exercises 85-90, find the value of each...Ch. 4.4 - Prob. 87PECh. 4.4 - Prob. 88PECh. 4.4 - For Exercises 85-90, find the value of each...Ch. 4.4 - Prob. 90PECh. 4.4 - Prob. 91PECh. 4.4 - For Exercises 91-94, verify the statement for the...Ch. 4.4 - For Exercises 91-94, verify the statement for the...Ch. 4.4 - For Exercises 91-94, verify the statement for the...Ch. 4.4 - For Exercises 95-96, give the exact values if...Ch. 4.4 - For Exercises 95-96, give the exact values if...Ch. 4.4 - Explain why neither sinnorcos can be greater than...Ch. 4.4 - Explain why tan is undefined at =2 but cot is...Ch. 4.4 - Prob. 99PECh. 4.4 - The circle shown is centered at the origin with a...Ch. 4.4 - Circle A, with radius a, and circle B , with...Ch. 4.5 - Graph the function and identify the key points on...Ch. 4.5 - Given fx=2sin4x, a. Identify the amplitude and...Ch. 4.5 - Given y=cos3x2, a. Identify the amplitude and...Ch. 4.5 - Given y=2cos3x+3, a. Identify the amplitude,...Ch. 4.5 - Given y=2sin6x2+1, a. Identify the amplitude,...Ch. 4.5 - A mechanical metronome uses an inverted pendulum...Ch. 4.5 - The value of sinx (increases/decreases) on 0,2...Ch. 4.5 - The value of cosx (increases/decreases) on 0,2...Ch. 4.5 - The graph of y=sinx and y=cosx differ by a...Ch. 4.5 - Given y=AsinBxC+D or y=AcosBxC+D , for B0 the...Ch. 4.5 - The sine function is an (even/odd) function...Ch. 4.5 - Given B0 , how would the equation y=AsinBxC+D be...Ch. 4.5 - Given B0 , how would the equation y=AcosBxC+D be...Ch. 4.5 - Given y=sinBx and y=cosBx , for B1 , is the period...Ch. 4.5 - From memory, sketch y=sinx on the interval 0,2 .Ch. 4.5 - Prob. 10PECh. 4.5 - For y=cosx , a. The domain is . b. The range is ...Ch. 4.5 - For y=sinx , a. The domain is . b. The range is ....Ch. 4.5 - a. Over what interval (s) taken between 0 and 2 is...Ch. 4.5 - a. Over what interval (s) taken between 0 and 2 is...Ch. 4.5 - Prob. 15PECh. 4.5 - For Exercises 15-16, identify the amplitude of the...Ch. 4.5 - By how many units does the graph of y=14cosx...Ch. 4.5 - By how many units does the graph of y=5sinx...Ch. 4.5 - For Exercises 19-24, graph the function and...Ch. 4.5 - For Exercises 19-24, graph the function and...Ch. 4.5 - Prob. 21PECh. 4.5 - For Exercises 19-24, graph the function and...Ch. 4.5 - For Exercises 19-24, graph the function and...Ch. 4.5 - For Exercises 19-24, graph the function and...Ch. 4.5 - For Exercises 25-26, identify the period. a. sin2x...Ch. 4.5 - Prob. 26PECh. 4.5 - For Exercises 27-32 a. Identify the amplitude and...Ch. 4.5 - For Exercises 27-32 a. Identify the amplitude and...Ch. 4.5 - For Exercises 27-32 a. Identify the amplitude and...Ch. 4.5 - For Exercises 27-32 a. Identify the amplitude and...Ch. 4.5 - For Exercises 27-32 a. Identify the amplitude and...Ch. 4.5 - For Exercises 27-32 a. Identify the amplitude and...Ch. 4.5 - Write a function of the form fx=AcosBx for the...Ch. 4.5 - Write a function of the form gx=AsinBx for the...Ch. 4.5 - Prob. 35PECh. 4.5 - A respiratory cycle is defined as the beginning of...Ch. 4.5 - Prob. 37PECh. 4.5 - For Exercises 37-38, identify the phase shift and...Ch. 4.5 - For Exercises 39-44, a. Identify the amplitude,...Ch. 4.5 - For Exercises 39-44, a. Identify the amplitude,...Ch. 4.5 - For Exercises 39-44, a. Identify the amplitude,...Ch. 4.5 - For Exercises 39-44, a. Identify the amplitude,...Ch. 4.5 - Prob. 43PECh. 4.5 - For Exercises 39-44, a. Identify the amplitude,...Ch. 4.5 - Write a function of the form fx=AcosBxC for the...Ch. 4.5 - Prob. 46PECh. 4.5 - Given y=2sin2x67 , a. Is the period less than or...Ch. 4.5 - Prob. 48PECh. 4.5 - For Exercises 49-52, rewrite the equation so that...Ch. 4.5 - For Exercises 49-52, rewrite the equation so that...Ch. 4.5 - For Exercises 49-52, rewrite the equation so that...Ch. 4.5 - For Exercises 49-52, rewrite the equation so that...Ch. 4.5 - Given y=2sin6x+23 , is the phase shift to the...Ch. 4.5 - Prob. 54PECh. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - Prob. 61PECh. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - Prob. 67PECh. 4.5 - For Exercises 55-68, a. Identify the amplitude,...Ch. 4.5 - The temperature TinF for Kansas City, Missouri,...Ch. 4.5 - The duration of daylight and darkness varies...Ch. 4.5 - The probability of precipitation in Modesto,...Ch. 4.5 - The monthly high temperature for Atlantic City....Ch. 4.5 - An adult human at rest inhales and exhales...Ch. 4.5 - The times for high and low tides are given in the...Ch. 4.5 - The data in the table represent the monthly power...Ch. 4.5 - The data in the table represent the duration of...Ch. 4.5 - For Exercises 77-78, write the range of the...Ch. 4.5 - For Exercises 77-78, write the range of the...Ch. 4.5 - Given fx=cosx and hx=3x+2 , find hfx and hfx , a....Ch. 4.5 - Given gx=sinx and kx=6x , find gkx and gkx a. Find...Ch. 4.5 - Prob. 81PECh. 4.5 - Write a function of the form y=AcosBxC+D that has...Ch. 4.5 - Write a function of the form y=AcosBxC+D that has...Ch. 4.5 - Write a function of the form y=AsinBxC+D that has...Ch. 4.5 - Prob. 85PECh. 4.5 - For Exercises 85-86 a. Write an equation of the...Ch. 4.5 - For Exercises 87-90, explain how to graph the...Ch. 4.5 - For Exercises 87-90, explain how to graph the...Ch. 4.5 - For Exercises 87-90, explain how to graph the...Ch. 4.5 - For Exercises 87-90, explain how to graph the...Ch. 4.5 - Prob. 91PECh. 4.5 - Is fx=cosx one-to-one? Explain why or why not.Ch. 4.5 - Prob. 93PECh. 4.5 - Explain why a function that is increasing on its...Ch. 4.5 - For Exercises 95-96, find the average rate of...Ch. 4.5 - For Exercises 95-96, find the average rate of...Ch. 4.5 - For exercises 97-100, use your knowledge of the...Ch. 4.5 - For exercises 97-100, use your knowledge of the...Ch. 4.5 - Prob. 99PECh. 4.5 - For exercises 97-100, use your knowledge of the...Ch. 4.5 - For Exercises 101-102, graph the piecewise-defined...Ch. 4.5 - For Exercises 101-102, graph the piecewise-defined...Ch. 4.5 - Functions a and m approximate the duration of...Ch. 4.5 - For Exercises 104-105, we demonstrate that...Ch. 4.5 - For Exercises 104-105, we demonstrate that...Ch. 4.5 - For Exercises 106-107, use a graph to solve the...Ch. 4.5 - For Exercises 106-107, use a graph to solve the...Ch. 4.5 - For Exercises 108-109, use a graph to solve the...Ch. 4.5 - Prob. 109PECh. 4.5 - Graph the functions on the window provided....Ch. 4.6 - Graph y=2sec4x .Ch. 4.6 - Graph y=cscx+2 .Ch. 4.6 - Graph y=4tan2x .Ch. 4.6 - Prob. 4SPCh. 4.6 - At values of x for which sinx=0 , the graph of...Ch. 4.6 - Prob. 2PECh. 4.6 - The relative maxima on the graph of y=sinx...Ch. 4.6 - Prob. 4PECh. 4.6 - If a function is an odd function, then each point...Ch. 4.6 - The range of y=tanx and y=cotx is .Ch. 4.6 - The graphs of both y=tanx and y=cotx are symmetric...Ch. 4.6 - For the functions y=AtanBxC and y=AcotBxC with B0...Ch. 4.6 - Sketch the graph of y=cscx from memory. Use the...Ch. 4.6 - Sketch the graph of y=secx from memory. Use the...Ch. 4.6 - For Exercises 11-16, identify the statements among...Ch. 4.6 - For Exercises 11-16, identify the statements among...Ch. 4.6 - For Exercises 11-16, identify the statements among...Ch. 4.6 - Prob. 14PECh. 4.6 - For Exercises 11-16, identify the statements among...Ch. 4.6 - For Exercises 11-16, identify the statements among...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - Prob. 19PECh. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - Prob. 23PECh. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - Prob. 30PECh. 4.6 - Prob. 31PECh. 4.6 - For Exercises 17-32, graph one period of the...Ch. 4.6 - For Exercises 33-34, write the range of the...Ch. 4.6 - Prob. 34PECh. 4.6 - Prob. 35PECh. 4.6 - Write a function of the form y=cscBxC for the...Ch. 4.6 - A plane flying at an altitude of 5mi travels on a...Ch. 4.6 - The distance dx (in feet) between an observer 30...Ch. 4.6 - a. Graph y=tanx on the interval , b. How many...Ch. 4.6 - a. Graph y=cotx on the interval , . b. How many...Ch. 4.6 - For Exercises 41-42, graph one complete period of...Ch. 4.6 - For Exercises 41-42, graph one complete period of...Ch. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - Prob. 47PECh. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - Prob. 50PECh. 4.6 - Prob. 51PECh. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - Prob. 56PECh. 4.6 - Prob. 57PECh. 4.6 - For Exercises 43-58, graph the function. (See...Ch. 4.6 - Write a function of the form y=tanBxC for the...Ch. 4.6 - Write a function of the form y=cotBx for the given...Ch. 4.6 - For Exercises 61-64, given y=fx and y=gx . a. Find...Ch. 4.6 - Prob. 62PECh. 4.6 - Prob. 63PECh. 4.6 - For Exercises 61-64, given y=fx and y=gx . a. Find...Ch. 4.6 - Prob. 65PECh. 4.6 - For Exercises 65-68, complete the statements for...Ch. 4.6 - For Exercises 65-68, complete the statements for...Ch. 4.6 - For Exercises 65-68, complete the statements for...Ch. 4.6 - Explain how to find two consecutive vertical...Ch. 4.6 - Prob. 70PECh. 4.6 - Prob. 71PECh. 4.6 - Prob. 72PECh. 4.6 - For Exercises 73-76, solve each equation for x on...Ch. 4.6 - Prob. 74PECh. 4.6 - Prob. 75PECh. 4.6 - For Exercises 73-76, solve each equation for x on...Ch. 4.6 - Show that the maximum length L (in feet) of a beam...Ch. 4.6 - Graph the functions y=tanx forx and y=xx33+2x515...Ch. 4.6 - Graph the functions y=secx and y=1+x22+5x424 on...Ch. 4.6 - Given fx=x2,gx=tanx, and hx=secx . a. Find fhx ....Ch. 4.6 - Given rx=x2,sx=cotx, and tx=cscx , a. Find rtx b....Ch. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - Prob. 2PRECh. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - Prob. 6PRECh. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - Prob. 9PRECh. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - Prob. 13PRECh. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.6 - For Exercises 1-16, identify which functions shown...Ch. 4.7 - Find the exact values or state that the expression...Ch. 4.7 - Find the exact values. a. cos11 b. tan133 c....Ch. 4.7 - Use a calculator to approximate the function...Ch. 4.7 - Use a calculator to approximate the degree measure...Ch. 4.7 - Find the exact values. a. coscos11 b. cos1cos43Ch. 4.7 - Find the exact value of sintan1125 .Ch. 4.7 - Find the exact value of cossin1211 .Ch. 4.7 - Write the expressiontansin1xx2+9 as an algebraic...Ch. 4.7 - For the construction of a house, a 16-ft by 6-ft...Ch. 4.7 - Approximate each expression in radians, rounded to...Ch. 4.7 - A function must be on its entire domain to have...Ch. 4.7 - If 23,12 is on the graph of y=cosx , what is the...Ch. 4.7 - The graph of y=tan1x has two ...Ch. 4.7 - The domain of y=arctanx is . The output is a real...Ch. 4.7 - In interval notation, the domain of y=cos1x is ....Ch. 4.7 - In interval notation, the domain ofy=sin1x is ....Ch. 4.7 - For Exercises 7-12, find the exact value or state...Ch. 4.7 - For Exercises 7-12, find the exact value or state...Ch. 4.7 - For Exercises 7-12, find the exact value or state...Ch. 4.7 - For Exercises 7-12, find the exact value or state...Ch. 4.7 - For Exercises 7-12, find the exact value or state...Ch. 4.7 - For Exercises 7-12, find the exact value or state...Ch. 4.7 - For Exercises 13-16, find the exact value....Ch. 4.7 - For Exercises 13-16, find the exact value....Ch. 4.7 - For Exercises 13-16, find the exact value....Ch. 4.7 - For Exercises 13-16, find the exact value....Ch. 4.7 - For Exercises 17-28, find the exact value or state...Ch. 4.7 - For Exercises 17-28, find the exact value or state...Ch. 4.7 - For Exercises 17-28, find the exact value or state...Ch. 4.7 - Prob. 20PECh. 4.7 - For Exercises 17-28, find the exact value or state...Ch. 4.7 - For Exercises 17-28, find the exact value or state...Ch. 4.7 - For Exercises 17-28, find the exact value or state...Ch. 4.7 - For Exercises 17-28, find the exact value or state...Ch. 4.7 - Prob. 25PECh. 4.7 - For Exercises 17-28, find the exact value or state...Ch. 4.7 - Prob. 27PECh. 4.7 - Prob. 28PECh. 4.7 - For Exercises 29-32, find the exact value....Ch. 4.7 - For Exercises 29-32, find the exact value....Ch. 4.7 - For Exercises 29-32, find the exact value....Ch. 4.7 - For Exercises 29-32, find the exact value....Ch. 4.7 - For Exercises 33-36, use a calculator to...Ch. 4.7 - For Exercises 33-36, use a calculator to...Ch. 4.7 - Prob. 35PECh. 4.7 - Prob. 36PECh. 4.7 - For Exercises 37-46, use a calculator to...Ch. 4.7 - For Exercises 37-46, use a calculator to...Ch. 4.7 - For Exercises 37-46, use a calculator to...Ch. 4.7 - For Exercises 37-46, use a calculator to...Ch. 4.7 - For Exercises 37-46, use a calculator to...Ch. 4.7 - For Exercises 37-46, use a calculator to...Ch. 4.7 - Prob. 43PECh. 4.7 - For Exercises 37-46, use a calculator to...Ch. 4.7 - Prob. 45PECh. 4.7 - For Exercises 37-46, use a calculator to...Ch. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - Prob. 50PECh. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - Prob. 57PECh. 4.7 - For Exercises 47-58, find the exact values. (See...Ch. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - Prob. 61PECh. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - Prob. 66PECh. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - For Exercises 59-70, find the exact values. (See...Ch. 4.7 - Prob. 70PECh. 4.7 - For Exercises 71-76, write the given expression as...Ch. 4.7 - For Exercises 71-76, write the given expression as...Ch. 4.7 - For Exercises 71-76, write the given expression as...Ch. 4.7 - For Exercises 71-76, write the given expression as...Ch. 4.7 - Prob. 75PECh. 4.7 - For Exercises 71-76, write the given expression as...Ch. 4.7 - To meet the requirements of the Americans with...Ch. 4.7 - A student measures the length of the shadow of the...Ch. 4.7 - A balloon advertising an open house is stabilized...Ch. 4.7 - A group of campers hikes down a steep path. One...Ch. 4.7 - Navajo Tube Hill, a snow tubing hill in Utah, is...Ch. 4.7 - A ski run on Giant Steps Mountain in Utah is 1475m...Ch. 4.7 - Prob. 83PECh. 4.7 - Prob. 84PECh. 4.7 - Show that sec1x=cos11x for x1 .Ch. 4.7 - Show that csc1x=sin11x for x1.Ch. 4.7 - Show that secx1+csc1x=2 for x1 .Ch. 4.7 - Prob. 88PECh. 4.7 - Prob. 89PECh. 4.7 - For Exercises 89-94, find the exact values. sec12Ch. 4.7 - Prob. 91PECh. 4.7 - Prob. 92PECh. 4.7 - For Exercises 89-94, find the exact values. cot13Ch. 4.7 - For Exercises 89-94, find the exact values. cot11Ch. 4.7 - For Exercises 95-100, use a calculator to...Ch. 4.7 - For Exercises 95-100, use a calculator to...Ch. 4.7 - For Exercises 95-100, use a calculator to...Ch. 4.7 - Prob. 98PECh. 4.7 - For Exercises 95-100, use a calculator to...Ch. 4.7 - For Exercises 95-100, use a calculator to...Ch. 4.7 - For Exercises 101-104, find the exact value if...Ch. 4.7 - Prob. 102PECh. 4.7 - For Exercises 101-104, find the exact value if...Ch. 4.7 - For Exercises 101-104, find the exact value if...Ch. 4.7 - Prob. 105PECh. 4.7 - For Exercises 105-108, find the inverse function...Ch. 4.7 - For Exercises 105-108, find the inverse function...Ch. 4.7 - For Exercises 105-108, find the inverse function...Ch. 4.7 - A video camera located at ground level follows the...Ch. 4.7 - The effective focal length f of a camera is the...Ch. 4.7 - For Exercises 111-114, use the relationship given...Ch. 4.7 - For Exercises 111-114, use the relationship given...Ch. 4.7 - Prob. 113PECh. 4.7 - For Exercises 111-114, use the relationship given...Ch. 4.7 - For Exercises 115-120, find the exact solution to...Ch. 4.7 - For Exercises 115-120, find the exact solution to...Ch. 4.7 - For Exercises 115-120, find the exact solution to...Ch. 4.7 - Prob. 118PECh. 4.7 - For Exercises 115-120, find the exact solution to...Ch. 4.7 - Prob. 120PECh. 4.7 - Prob. 121PECh. 4.7 - Explain the flaw in the logic:cos4=22 . Therefore,...Ch. 4.7 - Prob. 123PECh. 4.7 - Prob. 124PECh. 4.7 - In calculus, we can show that the area below the...Ch. 4.7 - Prob. 126PECh. 4.7 - The vertical viewing angle to a movie screen is...Ch. 4.7 - Prob. 128PECh. 4.7 - a. Graph the functions y=tan1x and y=xx33+x55 on...Ch. 4 - Convert 9628 to decimal degrees. Round to 2...Ch. 4 - Convert 225.24 to DMS (degree-minute-second) form....Ch. 4 - Convert 124 to radians. Give the answer in exact...Ch. 4 - Convert 73.8 to radians. Round to 2 decimal...Ch. 4 - Convert 58 radians to decimal degrees. Round to 1...Ch. 4 - For Exercises 6-8, find a positive angle...Ch. 4 - For Exercises 6-8, find a positive angle...Ch. 4 - For Exercises 6-8, find a positive angle...Ch. 4 - For Exercises 9-11, find a negative angle...Ch. 4 - For Exercises 9-11, find a negative angle...Ch. 4 - For Exercises 9-11, find a negative angle...Ch. 4 - Find an angle between 0 and 360 that is coterminal...Ch. 4 - Prob. 13RECh. 4 - A municide with a wheel diameter of 24in . moves...Ch. 4 - A pulley is 1.5ft in diameter. Find the distance...Ch. 4 - Seattle, Washington 47.61N,122.33W , and San...Ch. 4 - A spinning disk has radius of 10in . and rotates...Ch. 4 - A bicycle has wheels 26 inches in diameter. If the...Ch. 4 - A sprinkler rotates through an angle of 75...Ch. 4 - A round pie 10in. in diameter is cut into a slice...Ch. 4 - The real number t corresponds to the point P357,27...Ch. 4 - Identify the ordered pair on the unit circle...Ch. 4 - Identify the domain for each pair of functions. a....Ch. 4 - For Exercises 24-29, use the unit circle and the...Ch. 4 - For Exercises 24-29, use the unit circle and the...Ch. 4 - For Exercises 24-29, use the unit circle and the...Ch. 4 - For Exercises 24-29, use the unit circle and the...Ch. 4 - For Exercises 24-29, use the unit circle and the...Ch. 4 - For Exercises 24-29, use the unit circle and the...Ch. 4 - For Exercises 30-31, use the even -odd and...Ch. 4 - For Exercises 30-31, use the even -odd and...Ch. 4 - Write cost in terms of sint for t in Quadrant IV.Ch. 4 - Write cott in terms of csct for t in Quadrant II.Ch. 4 - Suppose that a right triangle C has legs of length...Ch. 4 - Determine the values of the six trigonometric...Ch. 4 - For Exercises 36-37, construct a right triangle to...Ch. 4 - For Exercises 36-37, construct a right triangle to...Ch. 4 - For Exercises 38-39, evaluate the expression...Ch. 4 - For Exercises 38-39, evaluate the expression...Ch. 4 - Given sin=99101 and cos=20101 , use the reciprocal...Ch. 4 - For Exercises 41-43, use an appropriate...Ch. 4 - For Exercises 41-43, use an appropriate...Ch. 4 - For Exercises 41-43, use an appropriate...Ch. 4 - For Exercises 44-45, given the function value,...Ch. 4 - For Exercises 44-45, given the function value,...Ch. 4 - Use a calculator to approximate the function...Ch. 4 - An observer at the top of a 48-ft building...Ch. 4 - During the first quarter moon, the Earth, Sun, and...Ch. 4 - Let P3,5 be a point on the terminal side of angle ...Ch. 4 - For Exercises 50-55, find the reference angle for...Ch. 4 - For Exercises 50-55, find the reference angle for...Ch. 4 - For Exercises 50-55, find the reference angle for...Ch. 4 - For Exercises 50-55, find the reference angle for...Ch. 4 - For Exercises 50-55, find the reference angle for...Ch. 4 - For Exercises 50-55, find the reference angle for...Ch. 4 - For Exercises 56-61, use reference angles to find...Ch. 4 - For Exercises 56-61, use reference angles to find...Ch. 4 - For Exercises 56-61, use reference angles to find...Ch. 4 - For Exercises 56-61, use reference angles to find...Ch. 4 - For Exercises 56-61, use reference angles to find...Ch. 4 - For Exercises 56-61, use reference angles to find...Ch. 4 - Identify which expressions are undefined. a....Ch. 4 - Given tan=23 and sin0 . Find sec .Ch. 4 - Given cos=37 and cot0 , find sin .Ch. 4 - Given sin=6061 and Quadrant III, find cot .Ch. 4 - For Exercises 66-69, determine the amplitude and...Ch. 4 - For Exercises 66-69, determine the amplitude and...Ch. 4 - For Exercises 66-69, determine the amplitude and...Ch. 4 - For Exercises 66-69, determine the amplitude and...Ch. 4 - For Exercises 70-72, graph one period of the...Ch. 4 - For Exercises 70-72, graph one period of the...Ch. 4 - For Exercises 70-72, graph one period of the...Ch. 4 - Determine the amplitude, period, and phase shift...Ch. 4 - For Exercises 74-75, graph one period of the...Ch. 4 - For Exercises 74-75, graph one period of the...Ch. 4 - For Exercises 76-77, determine the amplitude,...Ch. 4 - For Exercises 76-77, determine the amplitude,...Ch. 4 - For Exercises 78-79, graph one period of the...Ch. 4 - For Exercises 78-79, graph one period of the...Ch. 4 - The depth of water along a coastal inlet varies...Ch. 4 - The data in the table represent the percentage of...Ch. 4 - For Exercises 82-85, give the period of the...Ch. 4 - For Exercises 82-85, give the period of the...Ch. 4 - For Exercises 82-85, give the period of the...Ch. 4 - For Exercises 82-85, give the period of the...Ch. 4 - For Exercises 86-89, graph one period of the...Ch. 4 - For Exercises 86-89, graph one period of the...Ch. 4 - For Exercises 86-89, graph one period of the...Ch. 4 - For Exercises 86-89, graph one period of the...Ch. 4 - For Exercises 90-91, graph two periods of the...Ch. 4 - For Exercises 90-91, graph two periods of the...Ch. 4 - y=cot2xCh. 4 - y=cot2x+3Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - For Exercises 94-109, evaluate the expression....Ch. 4 - Use a calculator to approximate the function...Ch. 4 - For Exercises 111-114, use a calculator to...Ch. 4 - For Exercises 111-114, use a calculator to...Ch. 4 - For Exercises 111-114, use a calculator to...Ch. 4 - For Exercises 111-114, use a calculator to...Ch. 4 - Write the given expression as an algebraic...Ch. 4 - Find the lengths of sides a,b , and c to the...Ch. 4 - The length of the perpendicular line segment BP...Ch. 4 - Find the angle of repose for the pile of coarse...Ch. 4 - Convert 15.36 to DMS (degree-minute-second) form....Ch. 4 - Convert 130.3 to radians. Round to 2 decimal...Ch. 4 - Find the exact length of the arc intercepted by a...Ch. 4 - A skateboard designed for rough surfaces has...Ch. 4 - A pulley is 20 in. in diameter. Through how many...Ch. 4 - A circle has a radius of 9 yd. Find the area of a...Ch. 4 - For an acute angle if sin=56 evaluate cos and tan...Ch. 4 - Evaluate tan 6cot6 without the use of a...Ch. 4 - Given sin=513 , use a Pythagorean identity to find...Ch. 4 - Given sec75=2+6 , find a cofunction of another...Ch. 4 - Use a calculator to approximate sin sin211 to 4...Ch. 4 - A flag pole casts a shadow of 20 ft when the angle...Ch. 4 - A newly planted tree is anchored by a covered wire...Ch. 4 - For Exercises 14-21, evaluate the function or...Ch. 4 - For Exercises 14-21, evaluate the function or...Ch. 4 - For Exercises 14-21, evaluate the function or...Ch. 4 - For Exercises 14-21 evaluate the function or state...Ch. 4 - For Exercises 14-21 evaluate the function or state...Ch. 4 - For Exercises 14-21 evaluate the function or state...Ch. 4 - For Exercises 14-21 evaluate the function or state...Ch. 4 - For Exercises 14-21, evaluate the function or...Ch. 4 - Given sin=58 andcos0 , findtan .Ch. 4 - Given sec=43 and sin0 find csc .Ch. 4 - Given tan=43 and is in Quadrant IV, find sec .Ch. 4 - For Exercises 25-28, select the trigonometric...Ch. 4 - For Exercises 25-28, select the trigonometric...Ch. 4 - For Exercises 25-28, select the trigonometric...Ch. 4 - For Exercises 25-28, select the trigonometric...Ch. 4 - Use the even-odd and periodic properties of the...Ch. 4 - Suppose that a rectangle is bounded by the x-axis...Ch. 4 - For Exercises 31-32, determine the amplitude,...Ch. 4 - For Exercises 31-32, determine the amplitude,...Ch. 4 - For Exercises 33-36, graph one period of the...Ch. 4 - For Exercises 33-36, graph one period of the...Ch. 4 - For Exercises 33-36, graph one period of the...Ch. 4 - For Exercises 33-36, graph one period of the...Ch. 4 - Write a function of the form fx=AcosBx for the...Ch. 4 - Identify each statement as true or false. If a...Ch. 4 - For Exercises 39-40, graph one period of the...Ch. 4 - For Exercises 39-40, graph one period of the...Ch. 4 - For Exercises 41-42, graph two periods of the...Ch. 4 - For Exercises 41-42, graph two periods of the...Ch. 4 - Simplify each expression. a. sin132+cos122 b....Ch. 4 - Use a calculator to approximate the degree measure...Ch. 4 - Find the exact value of sin1sin116 .Ch. 4 - Find the exact value of tancos178Ch. 4 - Prob. 47TCh. 4 - Write the expression tancos1xx2+25 for x0 as an...Ch. 4 - A radar station tracks a plane flying at a...Ch. 4 - For Exercises 1-9, solve the equations and...Ch. 4 - Prob. 2CRECh. 4 - For Exercises 1-9, solve the equations and...Ch. 4 - For Exercises 1-9, solve the equations and...Ch. 4 - Prob. 5CRECh. 4 - Prob. 6CRECh. 4 - For Exercises 1-9, solve the equations and...Ch. 4 - Prob. 8CRECh. 4 - For Exercises 1-9, solve the equations and...Ch. 4 - Prob. 10CRECh. 4 - Given y=x2+2x4 a. Identify the vertex. b. Write...Ch. 4 - Given fx=x42x34x2+8x, a. Find the x -intercepts of...Ch. 4 - a. Graph y=3x2+x53x2 . b. Identify the asymptotes.Ch. 4 - Given y=2sin4x6, identify the a. Domain and range...Ch. 4 - Given fx=tanx and gx=x2 evaluate a. fog2 b. g+fCh. 4 - Prob. 16CRECh. 4 - Evaluate tanarcsin38 .Ch. 4 - Write the logarithm as the sum or difference of...Ch. 4 - Divide. Write the answer in standard form,...Ch. 4 - Suppose that y varies inversely as x and directly...
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- Total marks 15 4. : Let f R2 R be defined by f(x1, x2) = 2x²- 8x1x2+4x+2. Find all local minima of f on R². [10 Marks] (ii) Give an example of a function f R2 R which is neither bounded below nor bounded above, and has no critical point. Justify briefly your answer. [5 Marks]arrow_forward4. Let F RNR be a mapping. (i) x ЄRN ? (ii) : What does it mean to say that F is differentiable at a point [1 Mark] In Theorem 5.4 in the Lecture Notes we proved that if F is differentiable at a point x E RN then F is continuous at x. Proof. Let (n) CRN be a sequence such that xn → x ЄERN as n → ∞. We want to show that F(xn) F(x), which means F is continuous at x. Denote hnxn - x, so that ||hn|| 0. Thus we find ||F(xn) − F(x)|| = ||F(x + hn) − F(x)|| * ||DF (x)hn + R(hn) || (**) ||DF(x)hn||+||R(hn)||| → 0, because the linear mapping DF(x) is continuous and for all large nЄ N, (***) ||R(hn) || ||R(hn) || ≤ → 0. ||hn|| (a) Explain in details why ||hn|| → 0. [3 Marks] (b) Explain the steps labelled (*), (**), (***). [6 Marks]arrow_forward4. In Theorem 5.4 in the Lecture Notes we proved that if F: RN → Rm is differentiable at x = RN then F is continuous at x. Proof. Let (xn) CRN be a sequence such that x → x Є RN as n → ∞. We want F(x), which means F is continuous at x. to show that F(xn) Denote hn xnx, so that ||hn||| 0. Thus we find ||F (xn) − F(x) || (*) ||F(x + hn) − F(x)|| = ||DF(x)hn + R(hn)|| (**) ||DF(x)hn|| + ||R(hn) || → 0, because the linear mapping DF(x) is continuous and for all large n = N, |||R(hn) || ≤ (***) ||R(hn)|| ||hn|| → 0. Explain the steps labelled (*), (**), (***) [6 Marks] (ii) Give an example of a function F: RR such that F is contin- Total marks 10 uous at x=0 but F is not differentiable at at x = 0. [4 Marks]arrow_forward
- 3. Let f R2 R be a function. (i) Explain in your own words the relationship between the existence of all partial derivatives of f and differentiability of f at a point x = R². (ii) Consider R2 → R defined by : [5 Marks] f(x1, x2) = |2x1x2|1/2 Show that af af -(0,0) = 0 and -(0, 0) = 0, Jx1 მx2 but f is not differentiable at (0,0). [10 Marks]arrow_forward(1) Write the following quadratic equation in terms of the vertex coordinates.arrow_forwardThe final answer is 8/π(sinx) + 8/3π(sin 3x)+ 8/5π(sin5x)....arrow_forward
- Keity x२ 1. (i) Identify which of the following subsets of R2 are open and which are not. (a) A = (2,4) x (1, 2), (b) B = (2,4) x {1,2}, (c) C = (2,4) x R. Provide a sketch and a brief explanation to each of your answers. [6 Marks] (ii) Give an example of a bounded set in R2 which is not open. [2 Marks] (iii) Give an example of an open set in R2 which is not bounded. [2 Marksarrow_forward2. (i) Which of the following statements are true? Construct coun- terexamples for those that are false. (a) sequence. Every bounded sequence (x(n)) nEN C RN has a convergent sub- (b) (c) (d) Every sequence (x(n)) nEN C RN has a convergent subsequence. Every convergent sequence (x(n)) nEN C RN is bounded. Every bounded sequence (x(n)) EN CRN converges. nЄN (e) If a sequence (xn)nEN C RN has a convergent subsequence, then (xn)nEN is convergent. [10 Marks] (ii) Give an example of a sequence (x(n))nEN CR2 which is located on the parabola x2 = x², contains infinitely many different points and converges to the limit x = (2,4). [5 Marks]arrow_forward2. (i) What does it mean to say that a sequence (x(n)) nEN CR2 converges to the limit x E R²? [1 Mark] (ii) Prove that if a set ECR2 is closed then every convergent sequence (x(n))nen in E has its limit in E, that is (x(n)) CE and x() x x = E. [5 Marks] (iii) which is located on the parabola x2 = = x x4, contains a subsequence that Give an example of an unbounded sequence (r(n)) nEN CR2 (2, 16) and such that x(i) converges to the limit x = (2, 16) and such that x(i) # x() for any i j. [4 Marksarrow_forward
- 1. (i) which are not. Identify which of the following subsets of R2 are open and (a) A = (1, 3) x (1,2) (b) B = (1,3) x {1,2} (c) C = AUB (ii) Provide a sketch and a brief explanation to each of your answers. [6 Marks] Give an example of a bounded set in R2 which is not open. (iii) [2 Marks] Give an example of an open set in R2 which is not bounded. [2 Marks]arrow_forward2. if limit. Recall that a sequence (x(n)) CR2 converges to the limit x = R² lim ||x(n)x|| = 0. 818 - (i) Prove that a convergent sequence (x(n)) has at most one [4 Marks] (ii) Give an example of a bounded sequence (x(n)) CR2 that has no limit and has accumulation points (1, 0) and (0, 1) [3 Marks] (iii) Give an example of a sequence (x(n))neN CR2 which is located on the hyperbola x2 1/x1, contains infinitely many different Total marks 10 points and converges to the limit x = (2, 1/2). [3 Marks]arrow_forward3. (i) Consider a mapping F: RN Rm. Explain in your own words the relationship between the existence of all partial derivatives of F and dif- ferentiability of F at a point x = RN. (ii) [3 Marks] Calculate the gradient of the following function f: R2 → R, f(x) = ||x||3, Total marks 10 where ||x|| = √√√x² + x/2. [7 Marks]arrow_forward
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