Precalculus Examples

$\sec (\arctan (2))$

Step 1

Draw a triangle in the plane with vertices $(1, 2)$ , $(1, 0)$ , and the origin. Then $\arctan (2)$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(1, 2)$ . Therefore, $\sec (\arctan (2))$ is $\sqrt{1 + 2^{2}}$ .

$\sqrt{1 + 2^{2}}$

Step 2

Raise $2$ to the power of $2$ .

$\sqrt{1 + 4}$

Step 3

Add $1$ and $4$ .

$\sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$