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: 24


$\cos(-52^\circ14')$ is the cofunction in need to find here.

Work Step by Step

$$\sin(142^\circ14')$$ First, we must claim that cosine is the cofunction of sine. Then we find the complementary angle $\theta$ for cosine to rewrite $\sin(142^\circ14')$, which must satisfy $$\cos\theta=\sin(142^\circ14')\hspace{1cm}(1)$$ According to Cofunction Identity: $\cos\theta=\sin(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\sin(90^\circ-\theta)=\sin(142^\circ14')$$ $$90^\circ-\theta=142^\circ14'$$ $$\theta=90^\circ-142^\circ14'=-52^\circ14'$$ $\cos(-52^\circ14')$ is thus the cofunction in need to find here.
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