## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 1 - Precalculus Review - 1.4 Trigonometric Functions - Exercises - Page 30: 12

#### Answer

$\dfrac{\pi}{6}, \dfrac{5\pi}{6}$

#### Work Step by Step

Since $\csc{\theta}= \dfrac{1}{\sin{\{\theta}}$ As $\csc{\theta} = 2$ , we search figure 22 for points where the y-coordinate $(\sin{\theta}=\dfrac{1}{2})$ The two angles on the unit circle where $\sin{\theta}= \dfrac{1}{2}$ are $\dfrac{\pi}{6}$ and $\dfrac{5\pi}{6}$ $\theta= \dfrac{\pi}{6}, \dfrac{5\pi}{6}$

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