Precalculus Examples

$\tan (\arccos (\frac{π}{2}))$

Step 1

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

$\frac{\sqrt{(2 + π) (2 - π)}}{π}$