Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
4th Edition
ISBN: 9780134686974
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Chapter 7.4, Problem 46AYU
(a)
To determine
Toprove: Bretschneider’s Formula reduces to Heron’s Formula if a triangle is considered a quadrilateral with one side equal to
(b)
To determine
To calculate: The area of the lot for sale in a subdivision whose shape is a quadrilateral as shown below:
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EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Chapter 7 Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Ch. 7.1 - In a right triangle, if the length of the...Ch. 7.1 - Prob. 2AYUCh. 7.1 - Prob. 3AYUCh. 7.1 - Prob. 4AYUCh. 7.1 - Prob. 5AYUCh. 7.1 - Prob. 6AYUCh. 7.1 - True or False In a right triangle, if two sides...Ch. 7.1 - Prob. 8AYUCh. 7.1 - In Problems 9-18, find the exact value of the six...Ch. 7.1 - Prob. 10AYU
Ch. 7.1 - Prob. 11AYUCh. 7.1 - Prob. 12AYUCh. 7.1 - Prob. 13AYUCh. 7.1 - Prob. 14AYUCh. 7.1 - Prob. 15AYUCh. 7.1 - Prob. 16AYUCh. 7.1 - In Problems 9-18, find the exact value of the six...Ch. 7.1 - In Problems 9-18, find the exact value of the six...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - Prob. 22AYUCh. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - Prob. 26AYUCh. 7.1 - In Problems 19-28, find the exact value of each...Ch. 7.1 - Prob. 28AYUCh. 7.1 - In Problems 29-42, use the right triangle shown...Ch. 7.1 - Prob. 30AYUCh. 7.1 - Prob. 31AYUCh. 7.1 - Prob. 32AYUCh. 7.1 - Prob. 33AYUCh. 7.1 - In Problems 29-42, use the right triangle shown...Ch. 7.1 - Prob. 35AYUCh. 7.1 - Prob. 36AYUCh. 7.1 - In Problems 29-42, use the right triangle shown...Ch. 7.1 - Prob. 38AYUCh. 7.1 - Prob. 39AYUCh. 7.1 - Prob. 40AYUCh. 7.1 - Prob. 41AYUCh. 7.1 - Prob. 42AYUCh. 7.1 - Prob. 43AYUCh. 7.1 - Prob. 44AYUCh. 7.1 - Prob. 45AYUCh. 7.1 - Prob. 46AYUCh. 7.1 - Geometry A right triangle contains a 25 angle. (a)...Ch. 7.1 - Prob. 48AYUCh. 7.1 - Prob. 49AYUCh. 7.1 - Prob. 50AYUCh. 7.1 - Prob. 51AYUCh. 7.1 - Prob. 52AYUCh. 7.1 - Prob. 53AYUCh. 7.1 - Prob. 54AYUCh. 7.1 - Prob. 55AYUCh. 7.1 - Prob. 56AYUCh. 7.1 - Finding the Speed of a Truck A state trooper is...Ch. 7.1 - Prob. 58AYUCh. 7.1 - Prob. 59AYUCh. 7.1 - Parallax See Problem 59. 61 Cygni, sometimes...Ch. 7.1 - Prob. 61AYUCh. 7.1 - Prob. 62AYUCh. 7.1 - Prob. 63AYUCh. 7.1 - Prob. 64AYUCh. 7.1 - Prob. 65AYUCh. 7.1 - Prob. 66AYUCh. 7.1 - Constructing a Highway A highway whose primary...Ch. 7.1 - Photography A camera is mounted on a tripod 4 feet...Ch. 7.1 - Prob. 69AYUCh. 7.1 - Prob. 70AYUCh. 7.1 - Mt. Rushmore To measure the height of Lincoln’s...Ch. 7.1 - Prob. 72AYUCh. 7.1 - Chicago Skyscrapers The angle of inclination from...Ch. 7.1 - Prob. 74AYUCh. 7.1 - Prob. 75AYUCh. 7.1 - Shooting Free Throws in Basketball The eyes of a...Ch. 7.1 - Geometry Find the value of the angle in degrees...Ch. 7.1 - Surveillance Satellites A surveillance satellite...Ch. 7.1 - Prob. 79AYUCh. 7.1 - Prob. 80AYUCh. 7.1 - Explain how you would measure the height of a TV...Ch. 7.1 - The Gibb’s Hill Lighthouse, Southampton, Bermuda...Ch. 7.1 - Prob. 84AYUCh. 7.1 - Prob. 85AYUCh. 7.1 - Prob. 86AYUCh. 7.1 - Prob. 87AYUCh. 7.2 - The difference formula for the sine function is...Ch. 7.2 - Prob. 2AYUCh. 7.2 - Prob. 3AYUCh. 7.2 - Prob. 4AYUCh. 7.2 - Prob. 5AYUCh. 7.2 - Prob. 6AYUCh. 7.2 - Prob. 7AYUCh. 7.2 - Prob. 8AYUCh. 7.2 - In Problems 9-16, solve each triangle.Ch. 7.2 - Prob. 10AYUCh. 7.2 - In Problems 9-16, solve each triangle.
Ch. 7.2 - Prob. 12AYUCh. 7.2 - Prob. 13AYUCh. 7.2 - Prob. 14AYUCh. 7.2 - Prob. 15AYUCh. 7.2 - Prob. 16AYUCh. 7.2 - In problems 17-24, solve each triangle....Ch. 7.2 - Prob. 18AYUCh. 7.2 - Prob. 19AYUCh. 7.2 - Prob. 20AYUCh. 7.2 - Prob. 21AYUCh. 7.2 - Prob. 22AYUCh. 7.2 - Prob. 23AYUCh. 7.2 - Prob. 24AYUCh. 7.2 - Prob. 25AYUCh. 7.2 - Prob. 26AYUCh. 7.2 - In problems 25-36, two sides and an angle are...Ch. 7.2 - Prob. 28AYUCh. 7.2 - Prob. 29AYUCh. 7.2 - Prob. 30AYUCh. 7.2 - Prob. 31AYUCh. 7.2 - Prob. 32AYUCh. 7.2 - Prob. 33AYUCh. 7.2 - Prob. 34AYUCh. 7.2 - Prob. 35AYUCh. 7.2 - Prob. 36AYUCh. 7.2 - Finding the Length of a Ski Lift Consult the...Ch. 7.2 - Finding the Height of a Mountain Use the...Ch. 7.2 - Finding the Height of an Airplane An aircraft is...Ch. 7.2 - Finding the Height of the Bridge over the Royal...Ch. 7.2 - Prob. 41AYUCh. 7.2 - Distance between Runners Two runners in a marathon...Ch. 7.2 - Prob. 43AYUCh. 7.2 - Prob. 44AYUCh. 7.2 - Prob. 45AYUCh. 7.2 - Prob. 46AYUCh. 7.2 - Rescue at Sea Coast Guard Station Able is located...Ch. 7.2 - Prob. 48AYUCh. 7.2 - Finding the Lean of the Leaning Tower of Pisa The...Ch. 7.2 - Prob. 50AYUCh. 7.2 - Constructing a Highway A highway whose primary...Ch. 7.2 - Calculating Distances at Sea The navigator of a...Ch. 7.2 - Prob. 53AYUCh. 7.2 - Prob. 54AYUCh. 7.2 - Prob. 55AYUCh. 7.2 - Prob. 56AYUCh. 7.2 - The Original Ferris Wheel George Washington Gale...Ch. 7.2 - Mollweide’s Formula For any triangle, Mollweide’s...Ch. 7.2 - Prob. 61AYUCh. 7.2 - Prob. 62AYUCh. 7.2 - Prob. 63AYUCh. 7.2 - Prob. 64AYUCh. 7.2 - Prob. 65AYUCh. 7.2 - Prob. 66AYUCh. 7.2 - Prob. 67AYUCh. 7.2 - Prob. 68AYUCh. 7.2 - Prob. 69AYUCh. 7.2 - Prob. 70AYUCh. 7.2 - Prob. 71AYUCh. 7.2 - Prob. 72AYUCh. 7.3 - Write the formula for the distance d from to
....Ch. 7.3 - Prob. 2AYUCh. 7.3 - Prob. 3AYUCh. 7.3 - Prob. 4AYUCh. 7.3 - Prob. 5AYUCh. 7.3 - Prob. 6AYUCh. 7.3 - Prob. 7AYUCh. 7.3 - Prob. 8AYUCh. 7.3 - In Problems 9-16, solve each triangle.Ch. 7.3 - In Problems 9-16, solve each triangle.Ch. 7.3 - In Problems 9-16, solve each triangle.
Ch. 7.3 - Prob. 12AYUCh. 7.3 - Prob. 13AYUCh. 7.3 - Prob. 14AYUCh. 7.3 - Prob. 15AYUCh. 7.3 - Prob. 16AYUCh. 7.3 - Prob. 17AYUCh. 7.3 - Prob. 18AYUCh. 7.3 - Prob. 19AYUCh. 7.3 - Prob. 20AYUCh. 7.3 - Prob. 21AYUCh. 7.3 - Prob. 22AYUCh. 7.3 - Prob. 23AYUCh. 7.3 - Prob. 24AYUCh. 7.3 - Prob. 25AYUCh. 7.3 - Prob. 26AYUCh. 7.3 - Prob. 27AYUCh. 7.3 - Prob. 28AYUCh. 7.3 - Prob. 29AYUCh. 7.3 - Prob. 30AYUCh. 7.3 - Prob. 31AYUCh. 7.3 - Prob. 32AYUCh. 7.3 - Prob. 33AYUCh. 7.3 - Prob. 34AYUCh. 7.3 - Prob. 35AYUCh. 7.3 - Prob. 36AYUCh. 7.3 - Prob. 37AYUCh. 7.3 - Prob. 38AYUCh. 7.3 - Prob. 39AYUCh. 7.3 - Prob. 40AYUCh. 7.3 - Prob. 43AYUCh. 7.3 - Navigation An airplane flies due north from Ft....Ch. 7.3 - Avoiding a Tropical Storm A cruise ship maintains...Ch. 7.3 - Revising a Flight Plan In attempting to fly from...Ch. 7.3 - Major League Baseball Field A major league...Ch. 7.3 - Little League Baseball Field According to Little...Ch. 7.3 - Prob. 49AYUCh. 7.3 - Prob. 50AYUCh. 7.3 - Prob. 51AYUCh. 7.3 - Prob. 52AYUCh. 7.3 - Soccer Angles A soccer goal is 8 yards wide....Ch. 7.3 - Prob. 55AYUCh. 7.3 - Prob. 56AYUCh. 7.3 - Building a Swing Set Clint is building a wooden...Ch. 7.3 - Prob. 58AYUCh. 7.3 - Geometry Show that the length d of a chord of a...Ch. 7.3 - Prob. 60AYUCh. 7.3 - Prob. 61AYUCh. 7.3 - Prob. 62AYUCh. 7.3 - Prob. 63AYUCh. 7.3 - Prob. 64AYUCh. 7.3 - Prob. 65AYUCh. 7.3 - Prob. 66AYUCh. 7.3 - Prob. 67AYUCh. 7.3 - Prob. 68AYUCh. 7.3 - Prob. 69AYUCh. 7.3 - Prob. 70AYUCh. 7.3 - Prob. 71AYUCh. 7.4 - The area K of a triangle whose base is b and whose...Ch. 7.4 - Prob. 2AYUCh. 7.4 - Prob. 3AYUCh. 7.4 - Prob. 4AYUCh. 7.4 - Prob. 5AYUCh. 7.4 - Prob. 6AYUCh. 7.4 - Prob. 7AYUCh. 7.4 - Prob. 8AYUCh. 7.4 - Prob. 9AYUCh. 7.4 - Prob. 10AYUCh. 7.4 - Prob. 11AYUCh. 7.4 - Prob. 12AYUCh. 7.4 - Prob. 13AYUCh. 7.4 - Prob. 14AYUCh. 7.4 - Prob. 15AYUCh. 7.4 - Prob. 16AYUCh. 7.4 - Prob. 17AYUCh. 7.4 - Prob. 18AYUCh. 7.4 - Prob. 19AYUCh. 7.4 - Prob. 20AYUCh. 7.4 - Prob. 21AYUCh. 7.4 - Prob. 22AYUCh. 7.4 - Prob. 23AYUCh. 7.4 - Prob. 24AYUCh. 7.4 - Prob. 25AYUCh. 7.4 - Prob. 26AYUCh. 7.4 - Prob. 27AYUCh. 7.4 - Prob. 28AYUCh. 7.4 - Prob. 29AYUCh. 7.4 - Prob. 30AYUCh. 7.4 - Prob. 31AYUCh. 7.4 - Prob. 32AYUCh. 7.4 - Prob. 33AYUCh. 7.4 - Prob. 34AYUCh. 7.4 - Prob. 35AYUCh. 7.4 - Area of a Segment Find the area of the segment of...Ch. 7.4 - Prob. 37AYUCh. 7.4 - Prob. 38AYUCh. 7.4 - Prob. 39AYUCh. 7.4 - Prob. 40AYUCh. 7.4 - Prob. 41AYUCh. 7.4 - Prob. 42AYUCh. 7.4 - Prob. 43AYUCh. 7.4 - Bermuda Triangle The Bermuda Triangle is roughly...Ch. 7.4 - Prob. 45AYUCh. 7.4 - Prob. 46AYUCh. 7.4 - Perfect Triangles A perfect triangle is one having...Ch. 7.4 - Prob. 52AYUCh. 7.4 - Prob. 53AYUCh. 7.4 - Refer to Problem 109 in section 6.5. Show that the...Ch. 7.4 - Prob. 55AYUCh. 7.4 - Prob. 56AYUCh. 7.4 - Prob. 57AYUCh. 7.4 - Prob. 58AYUCh. 7.4 - Prob. 59AYUCh. 7.4 - Prob. 60AYUCh. 7.4 - Prob. 61AYUCh. 7.4 - Prob. 62AYUCh. 7.4 - Prob. 63AYUCh. 7.4 - Prob. 64AYUCh. 7.4 - Prob. 65AYUCh. 7.4 - Prob. 66AYUCh. 7.5 - The amplitude A and period T of f( x )=5sin( 4x )...Ch. 7.5 - Prob. 2AYUCh. 7.5 - Prob. 3AYUCh. 7.5 - Prob. 4AYUCh. 7.5 - In Problems 5-8, an object attached to a coiled...Ch. 7.5 - Prob. 6AYUCh. 7.5 - Prob. 7AYUCh. 7.5 - Prob. 8AYUCh. 7.5 - Rework Problem 7 under the same conditions, except...Ch. 7.5 - Rework Problem 8 under the same conditions, except...Ch. 7.5 - Rework Problem 9 under the same conditions, except...Ch. 7.5 - Rework Problem 10 under the same conditions,...Ch. 7.5 - Prob. 13AYUCh. 7.5 - Prob. 14AYUCh. 7.5 - Prob. 15AYUCh. 7.5 - Prob. 16AYUCh. 7.5 - Prob. 17AYUCh. 7.5 - Prob. 18AYUCh. 7.5 - Prob. 19AYUCh. 7.5 - Prob. 20AYUCh. 7.5 - Prob. 21AYUCh. 7.5 - Prob. 22AYUCh. 7.5 - Prob. 23AYUCh. 7.5 - Prob. 24AYUCh. 7.5 - Prob. 25AYUCh. 7.5 - Prob. 26AYUCh. 7.5 - Prob. 27AYUCh. 7.5 - Prob. 28AYUCh. 7.5 - Prob. 29AYUCh. 7.5 - Prob. 30AYUCh. 7.5 - Prob. 31AYUCh. 7.5 - Prob. 32AYUCh. 7.5 - Prob. 33AYUCh. 7.5 - Prob. 34AYUCh. 7.5 - Prob. 35AYUCh. 7.5 - Prob. 36AYUCh. 7.5 - Prob. 37AYUCh. 7.5 - Prob. 38AYUCh. 7.5 - Prob. 39AYUCh. 7.5 - Prob. 40AYUCh. 7.5 - Prob. 41AYUCh. 7.5 - Prob. 42AYUCh. 7.5 - Prob. 43AYUCh. 7.5 - Prob. 44AYUCh. 7.5 - Prob. 45AYUCh. 7.5 - Prob. 46AYUCh. 7.5 - Prob. 47AYUCh. 7.5 - Prob. 48AYUCh. 7.5 - Prob. 49AYUCh. 7.5 - Prob. 50AYUCh. 7.5 - Prob. 51AYUCh. 7.5 - Prob. 52AYUCh. 7.5 - Prob. 53AYUCh. 7.5 - Prob. 54AYUCh. 7.5 - Prob. 55AYUCh. 7.5 - Prob. 56AYUCh. 7.5 - Touch- Tone Phone On a Touch Tone Phone, each...Ch. 7.5 - Prob. 58AYUCh. 7.5 - Use a graphing utility to graph the function , ....Ch. 7.5 - Prob. 62AYUCh. 7.5 - Prob. 63AYUCh. 7.5 - Prob. 64AYUCh. 7.5 - Prob. 65AYUCh. 7.5 - Prob. 66AYUCh. 7.5 - Prob. 67AYUCh. 7.5 - If cos=45,02, find the exact value of: cos2 sin2...Ch. 7 - In Problems 1 and 2, find the exact value of the...Ch. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - In Problems 8-20, find the remaining angle(s) and...Ch. 7 - In Problems 8-20, find the remaining angle(s) and...Ch. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Constructing a Highway A highway whose primary...Ch. 7 - Approximating the Area of a Lake To approximate...Ch. 7 - Finding the Bearing of a Ship The Majesty leaves...Ch. 7 - Drive Wheels of an Engine The drive wheel of an...Ch. 7 - Prob. 38RECh. 7 - Simple Harmonic Motion An object attached to a...Ch. 7 - 43. The displacement d (in meter) of the bob of a...Ch. 7 - Find the exact value of the six trigonometric...Ch. 7 - Find the exact value of sin40cos50.Ch. 7 - In Problem 35, use the given information to...Ch. 7 - In Problem 35, use the given information to...Ch. 7 - In Problem 35, use the given information to...Ch. 7 - In Problem 68, solve each triangle. A=55, C=20,...Ch. 7 - In Problem 68, solve each triangle. a=3, b=7, A=40Ch. 7 - In Problem 68, solve each triangle. a=8, b=4, C=70Ch. 7 - Prob. 9CTCh. 7 - Prob. 10CTCh. 7 - Prob. 11CTCh. 7 - A hot- air balloon is flying at a height of 600...Ch. 7 - Prob. 13CTCh. 7 - Prob. 14CTCh. 7 - Madison wants to swim across Lake William from the...Ch. 7 - Prob. 16CTCh. 7 - Prob. 17CTCh. 7 - Prob. 18CTCh. 7 - Prob. 1CRCh. 7 - Prob. 2CRCh. 7 - Prob. 3CRCh. 7 - Prob. 4CRCh. 7 - Prob. 5CRCh. 7 - Prob. 6CRCh. 7 - Prob. 7CRCh. 7 - Prob. 8CRCh. 7 - Prob. 9CRCh. 7 - Prob. 10CRCh. 7 - Prob. 11CRCh. 7 - Prob. 12CRCh. 7 - Prob. 13CRCh. 7 - Prob. 14CR
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