Trigonometry Examples

$2 \sin (\frac{2 π}{3}) \cos (\frac{2 π}{3})$

Step 1

Apply the sine double-angle identity.

$\sin (2 \frac{2 π}{3})$

Step 2

Multiply $2 \frac{2 π}{3}$ .

Tap for more steps...

Step 2.1

Combine $2$ and $\frac{2 π}{3}$ .

$\sin (\frac{2 (2 π)}{3})$

Step 2.2

Multiply $2$ by $2$ .

$\sin (\frac{4 π}{3})$

Step 3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third 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:

$- 0.86602540 \dots$