Trigonometry Examples

$\cot (\arcsin (\frac{5}{6}))$

Step 1

Draw a triangle in the plane with vertices $(\sqrt{1^{2} - {(\frac{5}{6})}^{2}}, \frac{5}{6})$ , $(\sqrt{1^{2} - {(\frac{5}{6})}^{2}}, 0)$ , and the origin. Then $\arcsin (\frac{5}{6})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\sqrt{1^{2} - {(\frac{5}{6})}^{2}}, \frac{5}{6})$ . Therefore, $\cot (\arcsin (\frac{5}{6}))$ is $\frac{\sqrt{11}}{5}$ .

$\frac{\sqrt{11}}{5}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{11}}{5}$

Decimal Form:

$0.66332495 \dots$