Precalculus Examples

$\sec (\arccos (u))$

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

$\frac{1}{u}$