Answer
The solution on the interval $[0,2\pi )$, correct to four decimal places, is $1.8925$ or $5.0341$.
Work Step by Step
We have to calculate the equation using a calculator in radian mode:
$\theta ={{\tan }^{-1}}3\approx 1.2490$
Since, the tangent is negative in quadrants II and IV,
Thus,
$x\approx \pi -1.2490\ $
As, the value of $\pi $ is 3.14159.
Thus, the value of $x$ is:
$\begin{align}
& x\approx 3.14159-1.2490 \\
& \approx 1.8925
\end{align}$
or
$x\approx 2\pi -1.2490\ $
The value of $\pi $ is 3.14159.
Thus, the value of $x$ is:
$\begin{align}
& x\approx 2\times 3.14159-1.2490 \\
& \approx 6.28318-1.2490 \\
& \approx 5.0341
\end{align}$
Therefore, the solution of the equation $\tan x=-3$, correct to four decimal places, on the interval $[0,2\pi )$ is $1.8925$ or $5.0341$.
