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: 36


arccsc$(-\displaystyle \frac{1}{2})$ is not defined.

Work Step by Step

Inverse Cosecant Function: $y=\csc^{-1}x$ or $y=$ arccsc $x$ means that $x=\csc y$, for $-\displaystyle \frac{\pi}{2} \leq y \leq \frac{\pi}{2}$ , $y\neq 0$. ----------------- If there exists a y such that $\displaystyle \csc y=-\frac{1}{2}$, then, sine being reciprocal to csc, $\displaystyle \sin y=-\frac{2}{1}=-2$, which can not be for any y, since the range of sine is $[-1,1].$ So, arccsc$(-\displaystyle \frac{1}{2})$ is not defined.
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