# How do you find the exact value of cos [tan-1 (-2/3)]?

Jul 8, 2015

$\cos \left({\tan}^{- 1} \left(- \frac{2}{3}\right)\right) = \frac{3}{\sqrt{13}}$

#### Explanation:

If $\theta = {\tan}^{- 1} \left(- \frac{2}{3}\right)$
then we have the situation pictured below:

The hypotenuse is derived using the Pythagorean Theorem
and
The cos can be read directly from the diagram.