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: 28


$\cot(-84^\circ03')$ is the answer in this exercise.

Work Step by Step

$$\tan174^\circ03'$$ Cotangent and tangent are cofunctions. So to write $\tan174^\circ03'$ in terms of cofunction, cotangent would be included. Now the job is to figure out the value of $\theta$, which must satisfy $$\cot\theta=\tan174^\circ03'\hspace{1cm}(1)$$ According to Cofunction Identity: $\cot\theta=\tan(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\tan(90^\circ-\theta)=\tan174^\circ03'$$ $$90^\circ-\theta=174^\circ03'$$ $$\theta=90^\circ-174^\circ03'=-84^\circ03'$$ $\cot(-84^\circ03')$ is overall the answer to this exercise.
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