Answer
The solution of $\tan x=-\sqrt{3}$ in $[0,\pi )$ is $x=\pi -\frac{\pi }{3}$, or $x=\underline{\frac{2\pi }{3}}$. If n is any integer, all solutions of $\tan x=-\sqrt{3}$ are given by $\frac{2\pi }{3}+n\pi $.
Work Step by Step
To calculate another value of x:
$\begin{align}
& x=\pi -\frac{\pi }{3} \\
& =\frac{3\pi -\pi }{3} \\
& =\frac{2\pi }{3}
\end{align}$
Therefore, the value of x will be $\frac{2\pi }{3}$.
The interval $[0,\pi )$ covers the 1st and 2nd quadrants. The value of x is $\frac{2\pi }{3}$, according to the standard trigonometric general solution. Since, all the solutions for $\tan x=-\sqrt{3}$ can be written as $\frac{2\pi }{3}+n\pi $.
The value is considered to be $\pi $ because the interval has mentioned the limit of $[0,\pi )$.
Thus, the values of x will be $\frac{2\pi }{3}\,\text{ and }\,\frac{2\pi }{3}+n\pi $.
