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.

$0$