# How do you find tan (pi/3)?

Oct 24, 2014

Knowledge of special triangles is needed to solve this by hand.

$\frac{\pi}{3}$ is ${180}^{\circ} / 3 = {60}^{\circ}$

One of the special right triangles is ${30}^{\circ} {60}^{\circ} {90}^{\circ}$ where the sides have lengths with the following ratios.

${30}^{\circ} \implies x$
${60}^{\circ} \implies x \sqrt{3}$
${90}^{\circ} \implies 2 x$

If we let $x = 1$ then the side lengths are $1 , \sqrt{3} , \mathmr{and} 2$ respectively.

$\tan \left(\theta\right) = \frac{o p p o s i t e}{a \mathrm{dj} a c e n t} = \frac{y}{x}$

$\tan \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{1} = \sqrt{3}$