Trigonometry Examples

$\sin (2 \arccos (\frac{1}{2}))$

Step 1

The exact value of $\arccos (\frac{1}{2})$ is $\frac{π}{3}$ .

$\sin (2 \frac{π}{3})$

Step 2

Combine $2$ and $\frac{π}{3}$ .

$\sin (\frac{2 π}{3})$

Step 3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (\frac{π}{3})$

Step 4

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$