Explanation Given: The identity cos ( θ + π ) = − cos θ The given identity can be derived by using the identities listed below. Basic trigonometric identities : Pythagorean identity sin 2 x + cos 2 x = 1 Complementary angles 1. sin ( π 2 − x ) = cos x 2. cos ( π 2 − x ) = sin x Addition formulas 1. sin ( x + y ) = sin x cos y + cos x sin y 2. cos ( x + y ) = cos x cos y − sin x sin y Double-angle formulas 1. sin 2 x = 1 2 ( 1 − cos 2 x ) 2. cos 2 x = 1 2 ( 1 + cos 2 x ) 3. cos 2 x = cos 2 x − sin 2 x 4. sin 2 x = 2 sin x cos x Shift formulas 1. sin ( x + π 2 ) = cos x 2. cos ( x + π 2 ) = − sin x In the addition formula 2, we have cos ( x + y ) = cos x cos y − sin x sin y

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.4, Problem 51E

To determine

The derivation of the identity cos(θ+π)=−cosθ

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Chapter 1.4, Problem 50E

Chapter 1.4, Problem 52E

Chapter 1 Solutions

CALCULUS (CLOTH)

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The derivation of the identity cos ( θ + π ) = − cos θ

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The derivation of the identity cos(θ+π)=−cosθ

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