Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - Chapter Test - Page 503: 4


$sec~\theta=\frac{\sqrt {13}}{2}$ $cot~\theta=\frac{2}{3}$ $csc~\theta=\frac{\sqrt {13}}{3}$ $cos~\theta=\frac{2\sqrt {13}}{13}$ $sin~\theta=\frac{9\sqrt {13}}{13}$

Work Step by Step

$acute~angle:~(sin~\theta\gt0$ and $cos~\theta\gt0)$ $sec^2\theta=1+tan^2\theta=1+(\frac{3}{2})^2=\frac{13}{4}$ $sec~\theta=\frac{\sqrt {13}}{2}$ $cot~\theta=\frac{1}{tan~\theta}=\frac{1}{\frac{3}{2}}=\frac{2}{3}$ $csc^2\theta=cot^2\theta+1=(\frac{2}{3})^2+1=\frac{13}{9}$ $csc~\theta=\frac{\sqrt {13}}{3}$ $cos~\theta=\frac{1}{sec~\theta}=\frac{2}{\sqrt {13}}=\frac{2\sqrt {13}}{13}$ $sin~\theta=\frac{1}{csc~\theta}=\frac{9}{\sqrt {13}}=\frac{9\sqrt {13}}{13}$
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