Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 264: 45



Work Step by Step

The value of $\theta$ must be in the interval $[-90^o, 0^o) \cup (0^o, 90^o] $. $\theta=\csc^{-1}{\left(-2\right)}$ means that $\csc{\theta} = -2$. Since cosecant is the reciprocal of sine, then $\csc{\theta} = -2$ means $\sin{\theta}=-0.5$. Note that $\sin{30^o} = 0.5$. Since $\sin(-x)=-\sin{x}$, then $\sin{(-30^o)}=-\sin{30^o} = -0.5$ Thus, $\csc^{-1}{\left(-2\right)}=-30^o$
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