Trigonometry Examples

$\cot (\arccos (- 1))$

Step 1

Rewrite $\cot (\arccos (- 1))$ in terms of sines and cosines.

$\frac{\cos (\arccos (- 1))}{\sin (\arccos (- 1))}$

Step 2

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

$\frac{\cos (\arccos (- 1))}{\sqrt{1 + {(- 1)}^{3}}}$

Step 3

Raise $- 1$ to the power of $3$ .

$\frac{\cos (\arccos (- 1))}{\sqrt{1 - 1}}$

Step 4

Subtract $1$ from $1$ .

$\frac{\cos (\arccos (- 1))}{\sqrt{0}}$

Step 5

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

$\frac{\cos (\arccos (- 1))}{\sqrt{0^{2}}}$

Step 6

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

$\frac{\cos (\arccos (- 1))}{0}$

Step 7

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

Undefined