Trigonometry Examples

\tan (\arcsin (1))

$\tan (\arcsin (1))$

Step 1

Rewrite

\tan (\arcsin (1))

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

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

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

Step 2

Draw a triangle in the plane with vertices

(\sqrt{1^{2} - 1^{2}}, 1)

$(\sqrt{1^{2} - 1^{2}}, 1)$ ,

(\sqrt{1^{2} - 1^{2}}, 0)

$(\sqrt{1^{2} - 1^{2}}, 0)$ , and the origin. Then

\arcsin (1)

$\arcsin (1)$ is the angle between the positive x-axis and the ray beginning at the origin and passing through

(\sqrt{1^{2} - 1^{2}}, 1)

$(\sqrt{1^{2} - 1^{2}}, 1)$ . Therefore,

\cos (\arcsin (1))

$\cos (\arcsin (1))$ is

\sqrt{0}

$\sqrt{0}$ .

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

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

Step 3

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

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

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

Step 5

The expression contains a division by

0

$0$ . The expression is undefined.

Undefined