Answer
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 $4.9098$.
