Explanation Graph: Consider the provided equation, r = 5 − 2 sin θ Note that a curve is symmetric with respect to the line, θ = π 2 , if r , θ and r , π − θ have the same value, symmetric with respect to the polar axis if r , θ and r , − θ have the same value and symmetric with respect to the pole if r , θ and r , π + θ have the same value. First, check the symmetry with respect to the line θ = π 2 . Replace π − θ for θ and r for r in r = 5 − 2 sin θ and use sin π − θ = sin θ , r = 5 − 2 sin π − θ = 5 − 2 sin θ Since r , θ = r , π − θ , the curve is symmetric with respect to the line θ = π 2 . Now, check the symmetry with respect to the polar axis and use sin − θ = − sin θ . Replace − θ for θ and r for r in r = 5 − 2 sin θ , r = 5 − 2 sin − θ = 5 + 2 sin θ ≠ 5 − 2 sin θ Since r , θ ≠ r , − θ , the curve is not symmetric with respect to the polar axis. Now, check the symmetry with respect to the pole. Replace r for r and π + θ for θ in r = 5 − 2 sin θ and use sin π + θ = − sin θ , r = 5 − 2 sin π + θ r = 5 + 2 sin θ ≠ 5 − 2 sin θ Since r , θ ≠ − r , θ , the curve is not symmetric with respect to the pole. Hence, the curve is symmetric with respect to the line θ = π 2 , and θ lies in the interval π 2 ≤ θ ≤ 3 π 2 . Note that − 1 ≤ sin θ ≤ 1 . Thus, the maximum value occurs when sin θ = 1 . Calculate the maximum value of r . Substitute − 1 for sin θ in r = 5 − 2 sin θ , r = 5 − 2 − 1 = 5 + 2 = 7 Calculate the zero of the equation Let r = 0 . 5 − 2 sin θ = 0 2 sin θ = 5 sin θ = 5 2 = 2.5 This is not possible. Thus, there is no zero of the equation. Thus, the maximum value of r is 7 at θ = 3 π 2 and its zero does not exist

10th Edition

ISBN: 9781337879620

Author: Larson

Publisher: VST

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Chapter 6.8, Problem 34E

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To graph: The polar equation, r=5−2sinθ, by using symmetry, zeroes, and maximum r values.

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Chapter 6.8, Problem 33E

Chapter 6.8, Problem 35E

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Chapter 6 Solutions

EBK WEBASSIGN FOR LARSON'S TRIGONOMETRY

Ch. 6.1 - Find the inclination of (a) 4x5y=7 and (b) x+y=1.Ch. 6.1 - Prob. 2ECP Ch. 6.1 - Prob. 3ECP Ch. 6.1 - Find the distance between the point 3,2 and the...Ch. 6.1 - Prob. 5ECP Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E

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To graph: The polar equation, r = 5 − 2 sin θ , by using symmetry, zeroes, and maximum r values.

Solution Summary: The author explains how to graph the polar equation, r=5-2mathrmsintheta , using symmetry, zeroes, and maximum values.

To graph: The polar equation, r=5−2sinθ, by using symmetry, zeroes, and maximum r values.

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Chapter 6 Solutions