# How do you evaluate cos (arctan 3/4)?

Aug 16, 2016

$\frac{4}{5}$

#### Explanation:

Consider the right triangle ABC that has 2 legs, AB = 3, and BC = 4,
and $B = {90}^{\circ}$
Its hypotenuse AC is 5 (Ratio of sides --> 3:4:5)
The cosine of angle C is: $\cos C = \frac{B C}{A C} = \frac{4}{5}$
There for:
cos (arctan 3/4) = 4/5