## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 4 - Graphs of the Circular Functions - Section 4.3 Graphs of the Tangent and Cotangent Functions - 4.3 Exercises - Page 172: 49

#### Answer

The equation $c=tan~x$ has exactly four solutions in the interval $(-2\pi,2\pi]$

#### Work Step by Step

Suppose that $~~c~~$ is any number. In the interval $(-2\pi,-\pi]$, there is exactly one value of $x$ such that $c = tan~x$ In the interval $(-\pi,0]$, there is exactly one value of $x$ such that $c = tan~x$ In the interval $(0,\pi]$, there is exactly one value of $x$ such that $c = tan~x$ In the interval $(\pi,2\pi]$, there is exactly one value of $x$ such that $c = tan~x$ Therefore, in the interval $(-2\pi,2\pi]$, there are exactly four values of $x$ such that $c = tan~x$ The equation $c=tan~x$ has exactly four solutions in the interval $(-2\pi,2\pi]$

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