Trigonometry Examples

$\csc (\arccos (\frac{\sqrt{3}}{2}))$

Step 1

Draw a triangle in the plane with vertices $(\frac{\sqrt{3}}{2}, \sqrt{1^{2} - {(\frac{\sqrt{3}}{2})}^{2}})$ , $(\frac{\sqrt{3}}{2}, 0)$ , and the origin. Then $\arccos (\frac{\sqrt{3}}{2})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\frac{\sqrt{3}}{2}, \sqrt{1^{2} - {(\frac{\sqrt{3}}{2})}^{2}})$ . Therefore, $\csc (\arccos (\frac{\sqrt{3}}{2}))$ is $2$ .

$2$