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Q. 4

Expert-verified
Found in: Page 889

Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

Name the trigonometric functions that have asymptotes.

The trigonometric functions are $\mathrm{tan}x,secx,cscx,secx$

See the step by step solution

Step 1: Given information

Given trigonometric function

Step 2: Checking the asymptotes

For $y=\mathrm{tan}x$, the asymptotes are $x=\dots ,-\frac{3\pi }{2},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{2},\dots$

For $y=cotx$, the asymptotes are $x=\dots ,-2\pi ,-\pi ,0,\pi ,2\pi ,\dots$

For $y=cscx$, the asymptotes are $x=\dots ,-2\pi ,-\pi ,0,\pi ,2\pi ,\dots$

For $y=secx$, the asymptotes are $x=\dots ,-\frac{3\pi }{2},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{2},\dots$