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 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 218: 20


$\cos75^\circ$ is the cofunction needed to find.

Work Step by Step

$$\sin15^\circ$$ Cosine is the cofunction of sine. That means the question asks to write $\sin15^\circ$ in terms of sine and an angle. In other words, what is the value of $\theta$ with which $$\cos\theta=\sin15^\circ\hspace{1cm}(1)$$ According to Cofunction Identity: $\cos\theta=\sin(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\sin(90^\circ-\theta)=\sin15^\circ$$ $$90^\circ-\theta=15^\circ$$ $$\theta=90^\circ-15^\circ=75^\circ$$ Therefore $\cos75^\circ$ is the answer.
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