Trigonometry Examples

$\csc (\arctan (- 1))$

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

$- \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{2}$

Decimal Form:

$- 1.41421356 \dots$