Calculus Examples

$\sec (\arctan (3))$

Step 1

Draw a triangle in the plane with vertices $(1, 3)$ , $(1, 0)$ , and the origin. Then $\arctan (3)$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(1, 3)$ . Therefore, $\sec (\arctan (3))$ is $\sqrt{1 + 3^{2}}$ .

$\sqrt{1 + 3^{2}}$

Step 2

Raise $3$ to the power of $2$ .

$\sqrt{1 + 9}$

Step 3

Add $1$ and $9$ .

$\sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$