Precalculus Examples

$\csc (arccot (4))$

Step 1

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

$\sqrt{4^{2} + 1}$

Step 2

Raise $4$ to the power of $2$ .

$\sqrt{16 + 1}$

Step 3

Add $16$ and $1$ .

$\sqrt{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{17}$

Decimal Form:

$4.12310562 \dots$