Precalculus Examples

$\cot (arcsec (\sqrt{2}))$

Step 1

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

$1$