Trigonometry Examples

$\csc (\arctan (u))$

Step 1

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

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