Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 227: 46


$$\sin(\pi+x)=-\sin x$$

Work Step by Step

$$X=\sin(\pi+x)$$ According to the identity of the sum of sines: $$\sin(A+B)=\sin A\cos B+\cos A\sin B$$ Expand $X$: $$X=\sin\pi\cos x+\cos\pi\sin x$$ $$X=0\cos x+(-1)\sin x$$ $$X=-\sin x$$ Overall, $$\sin(\pi+x)=-\sin x$$
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