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: 33


We fill in the blank with $\cos$.

Work Step by Step

$$A33^\circ=\sin57^\circ\hspace{1cm}(1)$$ We notice that $$33^\circ+57^\circ=90^\circ$$ That means we can rewrite $(1)$ as $$A33^\circ=\sin(90-33^\circ)\hspace{1cm}(1)$$ Now from the Cofunction Identity: $$\cos\theta=\sin(90^\circ-\theta)$$ So $$A=\cos$$ In other words, we fill in the blank with $\cos$.
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