Trigonometry Examples

$\sin (arccsc (x))$

Step 1

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

$\frac{1}{x}$