Precalculus Examples

$\cot (\arcsin (\frac{8}{9}))$

Step 1

Draw a triangle in the plane with vertices $(\sqrt{1^{2} - {(\frac{8}{9})}^{2}}, \frac{8}{9})$ , $(\sqrt{1^{2} - {(\frac{8}{9})}^{2}}, 0)$ , and the origin. Then $\arcsin (\frac{8}{9})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\sqrt{1^{2} - {(\frac{8}{9})}^{2}}, \frac{8}{9})$ . Therefore, $\cot (\arcsin (\frac{8}{9}))$ is $\frac{\sqrt{17}}{8}$ .

$\frac{\sqrt{17}}{8}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{17}}{8}$

Decimal Form:

$0.51538820 \dots$