Trigonometry (11th Edition) Clone

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

Chapter 4 - Graphs of the Circular Functions - Section 4.4 Graphs of the Secant and Cosecant Functions - 4.4 Exercises - Page 180: 34



Work Step by Step

Figure 40 shows that the graph of $y=csc{x}$ is symmetric with respect to the origin. It can be seen from the figure that: (i) $\csc{(-\frac{3\pi}{2})}= 1$ while $\csc{(\frac{3\pi}{2})}=-1$ (ii) $\csc{(-\frac{\pi}{2})}=-1$ while $\csc{(\frac{\pi}{2})}=1$ In general, $\csc{(-x)}=-\csc{x}$. $\csc{x} = \sec{(-x)}$. Another way showing that $\csc{(-x)}=-\csc{x}$ is by using the concept of odd functions. Recall that when the graph of a function is symmetric with respect to the origin, then, the function is an odd function. If a function is odd, then $f(-x)=-f(x)$. Thus, since $y=\csc{x}$ is an odd function, then $\csc{(-x)}=-\csc{x}$ for all numbers within its domain.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.