Trigonometry Examples

\sin (- \frac{2 π}{3})

$\sin (- \frac{2 π}{3})$

Step 1

Add full rotations of

2 π

$2 π$ until the angle is greater than or equal to

0

$0$ and less than

2 π

$2 π$ .

\sin (\frac{4 π}{3})

$\sin (\frac{4 π}{3})$

Step 2

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})

$- \sin (\frac{π}{3})$

Step 3

The exact value of

\sin (\frac{π}{3})

$\sin (\frac{π}{3})$ is

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

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

- \frac{\sqrt{3}}{2}

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

Step 4

The result can be shown in multiple forms.

Exact Form:

- \frac{\sqrt{3}}{2}

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

Decimal Form:

- 0.86602540 \dots

$- 0.86602540 \dots$