Calculus Examples

$\csc (\arctan (x))$

Step 1

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

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