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 219: 46



Work Step by Step

$$A=\cos(\theta-270^\circ)$$ According to the identity of cosine difference: $$\cos(A-B)=\cos A\cos B+\sin A\sin B$$ $A$ would be: $$A=\cos\theta\cos270^\circ+\sin\theta\sin270^\circ$$ Remember that $\cos270^\circ=\cos(-90^\circ)=\cos90^\circ=0$, while $\sin270^\circ=\sin(-90^\circ)=-\sin90^\circ=-1$ That means, $$A=\cos\theta\times0+\sin\theta\times(-1)$$ $$A=-\sin\theta$$
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