Trigonometry Examples

$\sec (\arctan (v))$

Step 1

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

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