Precalculus Examples

$\sec (\arcsin (- \frac{\sqrt{3}}{2}))$

Step 1

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

$2$