Calculus 8th Edition

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

Appendix D - Trigonometry - D Exercises - Page A32: 31


$sin \phi=\frac{\sqrt 5}{3}$ $cos \phi=-\frac{2}{3}$ $tan \phi=-\frac{\sqrt 5}{2}$ $csc \phi=\frac{3\sqrt 5}{5}$ $cot \phi=-\frac{2\sqrt 5}{5}$

Work Step by Step

Since $sec \phi=-1.5=-\frac{3}{2}$, we can label the hypotenuse side as having length 3 and the adjacent side as having length 2. Then Pythagorean Theorem gives opposite side $=\sqrt {3^{2}-2^{2}}=\sqrt 5$ As $\frac{\pi}{2}0,cos\phi<0,tan\phi<0$ The other five trigonometric functions are given as follows: $sin \phi=\frac{\sqrt 5}{3}$ $cos \phi=-\frac{2}{3}$ $tan \phi=-\frac{\sqrt 5}{2}$ $csc \phi=\frac{3\sqrt 5}{5}$ $cot \phi=-\frac{2\sqrt 5}{5}$
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