Trigonometry Examples

$\cot (arccsc (2))$

Step 1

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

$\sqrt{2^{2} - 1}$

Step 2

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

$\sqrt{4 - 1}$

Step 3

Subtract $1$ from $4$ .

$\sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$