Trigonometry Examples

$\cos (\arcsin (\sqrt{\frac{2}{2}}))$

Step 1

Draw a triangle in the plane with vertices

$(\sqrt{1^{2} - {\sqrt{\frac{2}{2}}}^{2}}, \sqrt{\frac{2}{2}})$ ,

$(\sqrt{1^{2} - {\sqrt{\frac{2}{2}}}^{2}}, 0)$ , and the origin. Then

$\arcsin (\sqrt{\frac{2}{2}})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through

$(\sqrt{1^{2} - {\sqrt{\frac{2}{2}}}^{2}}, \sqrt{\frac{2}{2}})$ . Therefore,

$\cos (\arcsin (\sqrt{\frac{2}{2}}))$ 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.

$0$