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: 19


Write $\tan87^\circ$ in terms of the cofunction of the complementary angle: $$\cot3^\circ$$

Work Step by Step

$$\tan87^\circ$$ Cotangent is the cofunction of tangent. That means the question asks to write $\tan87^\circ$ in terms of cotangent and an angle. In other words, what is $\theta$ with which $$\cot\theta=\tan87^\circ\hspace{1cm}(1)$$ According to Cofunction Identity: $\cot\theta=\tan(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\tan(90^\circ-\theta)=\tan87^\circ$$ $$90^\circ-\theta=87^\circ$$ $$\theta=90^\circ-87^\circ=3^\circ$$ Therefore $\cot3^\circ$ is the answer.
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