Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises: 85

Answer

$\theta = 210^{\circ}$ $\theta = 330^{\circ}$

Work Step by Step

$csc ~\theta = -2$ $\frac{r}{y} = -2$ Since $r$ is not negative, we can let $r = 2$ and $y = -1$. We can find the angle $\alpha$ below the x-axis. $sin(\alpha) = \frac{1}{2}$ We know in a $30^{\circ}-60^{\circ}$ triangle, the side opposite the $30^{\circ}$ angle is 1 while the hypotenuse is 2. Therefore, $\alpha = 30^{\circ}$ Since $\alpha$ is the angle below the x-axis, then $\theta = 180^{\circ}+\alpha$ or $\theta = 360^{\circ}-\alpha$ $\theta = 210^{\circ}$ or $\theta = 330^{\circ}$
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