Precalculus Examples

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

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

Step 1

Draw a triangle in the plane with vertices

(1, \frac{12}{5})

$(1, \frac{12}{5})$ ,

(1, 0)

$(1, 0)$ , and the origin. Then

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

$\arctan (\frac{12}{5})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through

(1, \frac{12}{5})

$(1, \frac{12}{5})$ . Therefore,

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

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

\frac{5}{13}

$\frac{5}{13}$ .

\frac{5}{13}

$\frac{5}{13}$

Step 2

The result can be shown in multiple forms.

Exact Form:

\frac{5}{13}

$\frac{5}{13}$

Decimal Form:

0.\overline{384615}

$0.\overline{384615}$