Trigonometry Examples

$\tan (\arccos (1))$

Step 1

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

$\sqrt{0}$

Step 2

Rewrite $0$ as $0^{2}$ .

$\sqrt{0^{2}}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$0$