Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 2 - Section 2.2 - Calculators and Trigonometric Functions of an Acute Angle - 2.2 Problem Set - Page 73: 94

Answer

$\cot\theta=-\frac{4}{3},\sec\theta=-\frac{5}{4},\cos\theta=-\frac{4}{5},\sin\theta=\frac{3}{5},\csc\theta=\frac{5}{3}$

Work Step by Step

Since $\tan\theta=-\frac{3}{4}$, we have $\cot\theta=-\frac{4}{3}$ $\sec^{2}\theta=1+\tan^{2}\theta=1+\frac{9}{16}=\frac{25}{16}$ or $\sec\theta=-\frac{5}{4}$ ($\sec\theta$ will be negative since $\theta$ lies in second quadrant) Then, $\cos\theta=-\frac{4}{5}$ Further, we have $\sin\theta=\tan\theta\cos\theta=(-\frac{3}{4})\times(-\frac{4}{5})=\frac{3}{5}$ and $\csc\theta=\frac{5}{3}$
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