Trigonometry (11th Edition) Clone

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

Chapter 5 - Quiz (Sections 5.1-5.4) - Page 230: 4


Express $\cos(180^\circ-\theta)$ as a function of $\theta$ alone. $$\cos(180^\circ-\theta)=-\cos\theta$$

Work Step by Step

$$\cos(180^\circ-\theta)$$ To be expressed as a function of $\theta$ alone, we need here the identity for difference of cosines: $$\cos(A-B)=\cos A\cos B+\sin A\sin B$$ Apply it to $\cos(180^\circ-\theta)$, we have $$\cos(180^\circ-\theta)=\cos180^\circ\cos\theta+\sin180^\circ\sin\theta$$ $$\cos(180^\circ-\theta)=(-1)\times\cos\theta+0\times\sin\theta$$ $$\cos(180^\circ-\theta)=-\cos\theta$$ This is the ultimate function we need to find.
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