Algebra and Trigonometry
1st Edition
ISBN: 9781938168376
Author: Jay Abramson
Publisher: OpenStax
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Chapter 8.3, Problem 8TI
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Chapter 8 Solutions
Algebra and Trigonometry
Ch. 8.1 - Determine the period of the function g(x)=(cosx3)...Ch. 8.1 - What is the amplitude of the sinusoidal function...Ch. 8.1 - Determine the direction and magnitude of the phase...Ch. 8.1 - Determine the direction and magnitude of the...Ch. 8.1 - Determine the midline, amplitude, period, and...Ch. 8.1 - Determine the formula for the sine function in...Ch. 8.1 - Write a formula for the function graphed in figure...Ch. 8.1 - Sketch a graph of g(x)=0.8cos(2x) . Determine the...Ch. 8.1 - Draw a graph of g(x)=2cos(3x+6) . Determine the...Ch. 8.1 - What is the amplitude of the function f(x)=7cos(x)...
Ch. 8.1 - A weight is attached to a spring that is then hung...Ch. 8.1 - Why are the sine and cosine functions called...Ch. 8.1 - How does the graph of y=sinx compare with the...Ch. 8.1 - For the equation Acos(Bx+C)+D, what constants...Ch. 8.1 - How does the range of a translated sine function...Ch. 8.1 - How can the unit circle be used to construct the...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph two full...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - For the following exercises, graph one full period...Ch. 8.1 - Determine the amplitude, midline, period, and an...Ch. 8.1 - Determine the amplitude, period, midline and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - Determine the amplitude, period, midline, and an...Ch. 8.1 - For the following exercises, let f(x)=sinx . 31....Ch. 8.1 - For the following exercises, let f(x)=sinx . 32....Ch. 8.1 - For the following exercises, let f(x)=sinx . 33....Ch. 8.1 - For the following exercises, let f(x)=sinx . 34....Ch. 8.1 - For the following exercises, let f(x)=sinx . 35....Ch. 8.1 - For the following exercises, let f(x)=sinx . 36....Ch. 8.1 - For the following exercises, let f(x)=sinx . 37....Ch. 8.1 - For the following exercises, let f(x)=cosx. 38. On...Ch. 8.1 - For the following exercises, let f(x)=cosx. 39. On...Ch. 8.1 - For the following exercises, let f(x)=cosx. 40. On...Ch. 8.1 - For the following exercises, let f(x)=cosx. 41. On...Ch. 8.1 - For the following exercises, let f(x)=cosx 42. On...Ch. 8.1 - Graph h(x)=x+sinx on [0,2) . Explain why the graph...Ch. 8.1 - Graph h(x)=x+sinx on [100,100] . Did the graph...Ch. 8.1 - Graph f(x)=x+sinx on [0,2) and verbalize how the...Ch. 8.1 - Graph f(x)=x+sinx on the window [10,10] and...Ch. 8.1 - Graph f(x)=sinxx on the window [5,5] and explain...Ch. 8.1 - A Ferris wheel is 25 meters in diameter and...Ch. 8.2 - Sketch a graph of f(x)=3tan(6x) .Ch. 8.2 - How would the graph in Example 2 look different if...Ch. 8.2 - Find a formula for the function in Figure 5.Ch. 8.2 - Graph one period of f(x)=2.5sec(0.4x) .Ch. 8.2 - Graph one period of f(x)=6sec(4x+2)8 .Ch. 8.2 - Graph one period of f(x)=0.5csc(2x) .Ch. 8.2 - Given the graph of f(x)=2cos(2x)+1 shown in Figure...Ch. 8.2 - Explain how the graph of the sine function can be...Ch. 8.2 - How can the graph of y=cosx be used to construct...Ch. 8.2 - Explain why the period of tan x is equal .Ch. 8.2 - Why are there no intercepts on the graph of...Ch. 8.2 - How does the period of y=cscx compare with the...Ch. 8.2 - Find the following exercises, match each...Ch. 8.2 - Find the following exercises, match each...Ch. 8.2 - Find the following exercises, match each...Ch. 8.2 - Find the following exercises, match each...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, find the period and...Ch. 8.2 - For the following exercises, rewrite each...Ch. 8.2 - For the following exercises, rewrite each...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, sketch two periods of...Ch. 8.2 - For the following exercises, find and graph two...Ch. 8.2 - For the following exercises, find and graph two...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, find an equation for...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - For the following exercises, use a graphing...Ch. 8.2 - The function f(x)=20tan(10x) marks the distance in...Ch. 8.2 - Standing on the shore of a lake, a fisherman...Ch. 8.2 - A laser rangefinder is locked on a comet...Ch. 8.2 - A video camera is focused on a rocket on a...Ch. 8.3 - Given cos(0.5)0.8776 , write a relation involving...Ch. 8.3 - Evaluate each of the following. a. sin1(1) b....Ch. 8.3 - Evaluate cos1(0.4) using a calculator.Ch. 8.3 - Solve the triangle in Figure 9 for the angle .Ch. 8.3 - Evaluate tan1(tan(8)) and tan1(tan( 119)) .Ch. 8.3 - Evaluate cos1(sin( 114)) .Ch. 8.3 - Evaluate cos(tan1(5 12)) .Ch. 8.3 - Evaluate cos(sin1(79)) .Ch. 8.3 - Find a simplified expression for sin(tan1(4x)) for...Ch. 8.3 - Why do the functions f(x)=sin1x and g(x)=cos1x...Ch. 8.3 - Since the function y=cosx and y=cos1x are inverse...Ch. 8.3 - Explain the meaning of 6=arcsin(0.5) .Ch. 8.3 - Most calculators do not have a key to evaluate...Ch. 8.3 - Why must the domain of the sine function, sin x,...Ch. 8.3 - Discuss why this statement is incorrect:...Ch. 8.3 - Determine whether the following statement is true...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, use a calculator to...Ch. 8.3 - For the following exercises, find the angle in...Ch. 8.3 - For the following exercises, find the angle in...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value,...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, find the exact value...Ch. 8.3 - For the following exercises, evaluate the...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - For the following exercises, find the function if...Ch. 8.3 - Graph y=sin1x and state the domain and range of...Ch. 8.3 - Graph y=arccosx and state the domain and range of...Ch. 8.3 - Graph one cycle of y=tan1x and state the domain...Ch. 8.3 - For what value of x does sinx=sin1x ? Use a...Ch. 8.3 - For what value of x does cosx=cos1x ? Use a...Ch. 8.3 - Suppose a 13-foot ladder is leaning against a...Ch. 8.3 - Suppose you drive 0.6 miles on a road so that the...Ch. 8.3 - An isosceles triangle has two congruent sides of...Ch. 8.3 - Without using a calculator, approximate the value...Ch. 8.3 - A truss for the roof of a house is constructed...Ch. 8.3 - The line y=35x passes through the origin in the...Ch. 8.3 - The line y=37x passes through the origin in the...Ch. 8.3 - What percentage grade should a road have if the...Ch. 8.3 - A 20-foot ladder leans up against the side of a...Ch. 8.3 - Suppose a 15-foot ladder leans against the side of...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, graph two full...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, use this scenario:...Ch. 8 - For the following exercises, suppose a weight is...Ch. 8 - For the following exercises, suppose a weight is...Ch. 8 - For the following exercises, suppose a weight is...Ch. 8 - For the following exercises, suppose a weight is...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - For the following exercises, find the exact value...Ch. 8 - Graph f(x)=cosxand f(x)=secx on the interval [0,2)...Ch. 8 - Graph f(x)=sinx and f(x)=cscx and explain any...Ch. 8 - Graph the function f(x)=x1x33!+x55!x77! on the...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, sketch the graph of...Ch. 8 - For the following exercises, determine the...Ch. 8 - For the following exercises, determine the...Ch. 8 - For the following exercises, determine the...Ch. 8 - For the following exercises, find the amplitude,...Ch. 8 - For the following exercises, find the amplitude,...Ch. 8 - The outside temperature over the course of a day...Ch. 8 - Water is pumped into a storage bin and empties...Ch. 8 - For the following exercises, find the period and...Ch. 8 - For the following exercises, find the period and...Ch. 8 - Write the equation for the graph in Figure 1 in...Ch. 8 - If tanx=3 , find tan(x) .Ch. 8 - If secx=4 , find sec(x) .Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, graph the functions...Ch. 8 - For the following exercises, let f(x)=35cos(6x) ....Ch. 8 - For the following exercises, let f(x)=35cos(6x) ....Ch. 8 - For the following exercises, let f(x)=35cos(6x) ....Ch. 8 - For the following exercises, find and graph one...Ch. 8 - For the following exercises, find and graph one...Ch. 8 - For the following exercises, graph the function....Ch. 8 - For the following exercises, graph the function....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, find the exact value....Ch. 8 - For the following exercises, suppose sint=xx+1 ....Ch. 8 - For the following exercises, suppose sint=xx+1 ....Ch. 8 - Given Figure 2, find the measure of angle to...Ch. 8 - For the following exercises, determine whether the...Ch. 8 - For the following exercises, determine whether the...Ch. 8 - The grade of a road is 7%. This means that for...
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- Question 10 (5 points) (07.04 MC) Vectors u and v are shown in the graph. -12-11 -10 -9 -8 -7 -6 -5 What is proju? a -6.5i - 4.55j b -5.2i+2.6j с -4.7631 3.334j d -3.81i+1.905j < + 10 6 5 4 3 2 -3 -2 -10 1 -1 -2 -3 u -4 -5 -6 -7arrow_forwardFind the lengths of PR and OR in terms of the angles α and β. Find the angles ∠ONQ and ∠NPQ. Find the lengths of ON and PN in terms of the angle β. Find the length of PQ. Find the length of QR. Find the length of OM. Find the length of RM. What formula can you write down by noting that PR = QR + PQ? What formula can you write down by noting that OR = OM - RM?arrow_forward5) Solve the triangle. 2 95° 4 B с A) c=3.63, A=59.5°, B = 25.5° C) c = 4.63, A = 59.5°, B = 25.5° A B) c 4.63, A 25.5°, B = 59.5° = = D) c 5.63, A = 25.5°, B = 59.5°arrow_forward
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- 18) Find all the complex cube roots of - 8i. Leave your answers in polar form with the argument in degrees.arrow_forwardWrite the complex number √3 - i in polar form.arrow_forward2 10) The letters x and y represent rectangular coordinates. Write the equation x² + 4y = 4 using polar coordinates (r, e). A) 4 cos² 0 + sin² 0 = 4r C) r²(4 cos² 0 + sin² 0) = 4 B) cos² 0 + 4 sin² 0 = 4r D) r² (cos20 + 4 sin² 0) = 4arrow_forward
- 2) A radio transmission tower is 130 feet tall. How long should a guy wire be if it is to be attached 6 feet from the top and is to make an angle of 20° with the ground? Give your answer to the nearest tenth of a foot.arrow_forward4) Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. b=6, c=7, B = 80° A) one triangle B=40°, A = 60°, a = 13 C) one triangle C 39°, A 61°, a = 15 = B) one triangle C=41°, A = 59°, a = 17 D) no trianglearrow_forward7) A painter needs to cover a triangular region 63 meters by 67 meters by 74 meters. A can of paint covers 70 square meters. How many cans will be needed?arrow_forward
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