Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Review Exercises - Page 242: 17

Answer

$$\cos210^\circ=\cos150^\circ\cos60^\circ-\sin150^\circ\sin60^\circ$$ 17 is matched with I.

Work Step by Step

$$\cos210^\circ$$ We can write $210^\circ$ as the sum of $150^\circ$ and $60^\circ$. Thus, $$\cos210^\circ=\cos(150^\circ+60^\circ)$$ Here we can apply the sum identity for cosine for $\cos(150^\circ+60^\circ)$. $$\cos(A+B)=\cos A\cos B-\sin A\sin B$$ So, if we replace $A=150^\circ$ and $B=60^\circ$, we would have $$\cos210^\circ=\cos150^\circ\cos60^\circ-\sin150^\circ\sin60^\circ$$ This fits with choice I. Therefore, we should match 17 with I.
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