# Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 90

The solution on the interval $[0,2\pi )$, correct to four decimal places, is $1.7682$ or $4.9098$.

#### Work Step by Step

We have to calculate the equation using a calculator in radian mode: $\theta ={{\tan }^{-1}}5\approx 1.3734$ Since, the tangent is negative in quadrants II and IV, Thus, $x\approx \pi -1.3734\$ The value of $\pi$ is 3.14159. Thus, the value of $x$ is \begin{align} & x\approx 3.14159-1.3734 \\ & \approx 1.7682 \end{align} or \begin{align} & x\approx 2\times 3.14159-1.3734 \\ & \approx 6.28318-1.3734 \\ & \approx 4.9098 \end{align} Therefore, the solution of the equation $\tan x=-5$, correct to four decimal places, on the interval $[0,2\pi )$ is $1.7682$ or $4.9098$.

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