Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 1 - Review Exercises: 40

Answer

$\sin\theta=\frac{y}{r}=\frac{\sqrt {3}}{5}$ $\cos\theta=\frac{x}{r}=\frac{-\sqrt {22}}{5}=-\frac{\sqrt {22}}{5}$ $\csc\theta=\frac{r}{y}=\frac{5}{\sqrt {3}}=\frac{5\sqrt 3}{3}$ $\sec\theta=\frac{r}{x}=\frac{5}{-\sqrt {22}}=-\frac{5\sqrt {22}}{22}$ $\tan\theta=\frac{y}{x}=\frac{\sqrt {3}}{-\sqrt {22}}=-\frac{\sqrt {66}}{22}$ $\cot\theta=\frac{x}{y}=\frac{-\sqrt {22}}{\sqrt {3}}=-\frac{\sqrt {66}}{3}$

Work Step by Step

From sine we know that $y=\sqrt 3; r=5$, so lets find x: $x^{2}+y^{2}=r^{2}$ $x^{2}+(\sqrt 3)^{2}=5^{2}$ $x^{2}+3=25$ $x^{2}=22$ (since $\cos\theta\lt0$) $x=\sqrt {22}$
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