Precalculus Examples

$\cot (\arcsin (\frac{2}{5}))$

Step 1

Draw a triangle in the plane with vertices $(\sqrt{1^{2} - {(\frac{2}{5})}^{2}}, \frac{2}{5})$ , $(\sqrt{1^{2} - {(\frac{2}{5})}^{2}}, 0)$ , and the origin. Then $\arcsin (\frac{2}{5})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\sqrt{1^{2} - {(\frac{2}{5})}^{2}}, \frac{2}{5})$ . Therefore, $\cot (\arcsin (\frac{2}{5}))$ is $\frac{\sqrt{21}}{2}$ .

$\frac{\sqrt{21}}{2}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{21}}{2}$

Decimal Form:

$2.29128784 \dots$