Trigonometry Examples

$\cot (\arctan (\frac{x}{\sqrt{3}}))$

Step 1

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

$\frac{1}{\frac{x}{\sqrt{3}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{\sqrt{3}}{x}$

Step 3

Multiply $\frac{\sqrt{3}}{x}$ by $1$ .

$\frac{\sqrt{3}}{x}$