Explanation Given information: sin θ = cos 2 θ for 0 ≤ θ < 2 π Formula used: sin θ = sin ( π 2 − 2 θ ) Calculation: Given that sin θ = cos 2 θ for 0 ≤ θ < 2 π Or, sin θ = sin ( π 2 − 2 θ ) We must find the angle θ such that sin θ = sin ( π 2 − 2 θ ) . First let’s determine when angle θ 1 and θ 2 satisfy sin t 1 = sin θ 2 . Figure shows that this occurs if θ 2 = θ 1 or θ 2 = π − θ 1 . Since the since function is periodic with period 2 π . Sin θ 2 = sin θ 1 ⇔ θ 2 = θ 1 + 2 π k Or, θ 2 = π − θ 1 + 2 π k Where k is an integer

4th Edition

ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

Chapter 1.4, Problem 46E

To determine

To solve:

The equation sinθ=cos2θ for 0≤θ<2π.

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Chapter 1.4, Problem 45E

Chapter 1.4, Problem 47E

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Chapter 1 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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