Trigonometry Examples

$\sin (\arccos (- \frac{4}{5}))$

Step 1

Draw a triangle in the plane with vertices $(- \frac{4}{5}, \sqrt{1^{2} - {(- \frac{4}{5})}^{2}})$ , $(- \frac{4}{5}, 0)$ , and the origin. Then $\arccos (- \frac{4}{5})$ is the angle between the positive x-axis and the ray beginning at the origin and passing through $(- \frac{4}{5}, \sqrt{1^{2} - {(- \frac{4}{5})}^{2}})$ . Therefore, $\sin (\arccos (- \frac{4}{5}))$ is $\sqrt{\frac{9}{25}}$ .

$\sqrt{\frac{9}{25}}$

Step 2

Rewrite $\sqrt{\frac{9}{25}}$ as $\frac{\sqrt{9}}{\sqrt{25}}$ .

$\frac{\sqrt{9}}{\sqrt{25}}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2}}}{\sqrt{25}}$

Step 3.2

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

$\frac{3}{\sqrt{25}}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Rewrite $25$ as $5^{2}$ .

$\frac{3}{\sqrt{5^{2}}}$

Step 4.2

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

$\frac{3}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$