Question

How do you find the value of $\tan \left(\frac{\mathrm{\pi }}{3}\right)$?

Answer 1

Calculate the value of trigonometric ratio at given angle:

Let $x$ be the value of $\tan \left(\frac{\mathrm{\pi }}{3}\right)$.

$\therefore x=\tan \left(\frac{\mathrm{\pi }}{3}\right)$

We know that $\mathbf{\pi }\mathbf{=}\mathbf{180}\mathbf{°}$

$\therefore x=\tan \left(\frac{\mathrm{\pi }}{3}\right)$

$=\tan \frac{180°}{3}$

$=\tan 60°$

$=\frac{\sin 60°}{\cos 60°}$ $\left[\because tan\theta =\frac{sin\theta }{cos\theta }\right]$

$=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$ $\left[\because sin60°=\frac{\sqrt{3}}{2};cos60°=\frac{1}{2}\right]$

$=\sqrt{3}$

Hence, the value of $\mathit{t}\mathit{a}\mathit{n}\left(\frac{\pi }{3}\right)$ is $\sqrt{\mathbf{3}}$.