Precalculus Examples

$\cot (\arctan (\frac{1}{x}))$

Step 1

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

$\frac{1}{\frac{1}{x}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 x$

Step 3

Multiply $x$ by $1$ .

$x$