Trigonometry Examples

$\tan (\arcsin (1))$

Step 1

Rewrite $\tan (\arcsin (1))$ in terms of sines and cosines.

$\frac{\sin (\arcsin (1))}{\cos (\arcsin (1))}$

Step 2

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

$\frac{\sin (\arcsin (1))}{\sqrt{0}}$

Step 3

Rewrite $0$ as $0^{2}$ .

$\frac{\sin (\arcsin (1))}{\sqrt{0^{2}}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$\frac{\sin (\arcsin (1))}{0}$

Step 5

The expression contains a division by $0$ . The expression is undefined.

Undefined