Precalculus Examples

$\cos (\arcsin (\frac{7}{8}))$

Step 1

Draw a triangle in the plane with vertices $(\sqrt{1^{2} - {(\frac{7}{8})}^{2}}, \frac{7}{8})$ , $(\sqrt{1^{2} - {(\frac{7}{8})}^{2}}, 0)$ , and the origin. Then $\arcsin (\frac{7}{8})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(\sqrt{1^{2} - {(\frac{7}{8})}^{2}}, \frac{7}{8})$ . Therefore, $\cos (\arcsin (\frac{7}{8}))$ is $\sqrt{\frac{15}{64}}$ .

$\sqrt{\frac{15}{64}}$

Step 2

Rewrite $\sqrt{\frac{15}{64}}$ as $\frac{\sqrt{15}}{\sqrt{64}}$ .

$\frac{\sqrt{15}}{\sqrt{64}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $64$ as $8^{2}$ .

$\frac{\sqrt{15}}{\sqrt{8^{2}}}$

Step 3.2

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

$\frac{\sqrt{15}}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{15}}{8}$

Decimal Form:

$0.48412291 \dots$