Trigonometry Examples

$\csc (arccot (- \frac{2}{1}))$

Step 1

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

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

Step 2

Raise $- 2$ to the power of $2$ .

$\sqrt{4 + 1}$

Step 3

Add $4$ and $1$ .

$\sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$