Precalculus Examples

$\cos (\arctan (\frac{12}{5}))$

Step 1

Draw a triangle in the plane with vertices $(1, \frac{12}{5})$ , $(1, 0)$ , and the origin. Then $\arctan (\frac{12}{5})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(1, \frac{12}{5})$ . Therefore, $\cos (\arctan (\frac{12}{5}))$ is $\frac{5}{13}$ .

$\frac{5}{13}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{13}$

Decimal Form:

$0.\overline{384615}$