Precalculus Examples

$\sec (\arccos (x))$

Step 1

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

$\frac{1}{x}$