Trigonometry Examples

$\tan (\arcsin (\frac{3}{5}))$

Step 1

Draw a triangle in the plane with vertices $(\sqrt{1^{2} - {(\frac{3}{5})}^{2}}, \frac{3}{5})$ , $(\sqrt{1^{2} - {(\frac{3}{5})}^{2}}, 0)$ , and the origin. Then $\arcsin (\frac{3}{5})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\sqrt{1^{2} - {(\frac{3}{5})}^{2}}, \frac{3}{5})$ . Therefore, $\tan (\arcsin (\frac{3}{5}))$ is $\frac{3}{4}$ .

$\frac{3}{4}$

Step 2

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$