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: 30


$\cos(-8.0142^\circ)$ is the answer to this exercise.

Work Step by Step

$$\sin98.0142^\circ$$ As cosine and sine are cofunctions, $\cos\theta$ is the cofunction needed to find as long as $\theta$ satisfies $$\cos\theta=\sin98.0142^\circ\hspace{1cm}(1)$$ According to Cofunction Identity: $\tan\theta=\cot(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\sin(90^\circ-\theta)=\sin98.0142^\circ$$ $$90^\circ-\theta=98.0142^\circ$$ $$\theta=90^\circ-98.0142^\circ=-8.0142^\circ$$ Hence, $\cos(-8.0142^\circ)$ is the answer to this exercise.
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