Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises: 34

Answer

$sin\theta=-\frac{3}{4}$ $cos\theta=\frac{\sqrt 7}{4}$ $tan\theta=-\frac{3}{ \sqrt 7}=-\frac{3\sqrt 7}{ 7}$ $sec \theta=\frac{4}{\sqrt 7}=\frac{4\sqrt 7}{ 7}$ $cot\theta=-\frac{\sqrt 7}{ 3}$

Work Step by Step

Since $csc\theta=-\frac{4}{3}$, we can label the hypotenuse side as having length 4 and the opposite side as having length 3. Then Pythagorean Theorem gives adjacent side $=\sqrt {4^{2}-3^{2}}=\sqrt 7$ As $\frac{3\pi}{2}0,tan\theta<0$ The other five trigonometric functions are given as follows: $sin\theta=-\frac{3}{4}$ $cos\theta=\frac{\sqrt 7}{4}$ $tan\theta=-\frac{3}{ \sqrt 7}=-\frac{3\sqrt 7}{ 7}$ $sec \theta=\frac{4}{\sqrt 7}=\frac{4\sqrt 7}{ 7}$ $cot\theta=-\frac{\sqrt 7}{ 3}$
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