Trigonometry Examples

$\cos (arcsec (u))$

Step 1

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

$\frac{1}{u}$