# How do you find sin if tan=2?

Nov 27, 2015

Ans: $\pm \frac{2 \sqrt{5}}{5}$
Use the trig identity: ${\sin}^{2} x = \frac{1}{1 + {\cot}^{2} x}$
$\tan x = 2$ --> $\cot x = \frac{1}{2}$ --> ${\cot}^{2} x = \frac{1}{4}$
${\sin}^{2} x = \frac{1}{1 + \frac{1}{4}} = \frac{1}{\frac{5}{4}} = \frac{4}{5}$
$\sin x = \pm \frac{2}{\sqrt{5}} = \pm \frac{2 \sqrt{5}}{5}$