Trigonometry Examples

$\sin (- \frac{4}{3} \cdot π)$

Step 1

Combine $π$ and $\frac{4}{3}$ .

$\sin (- \frac{π \cdot 4}{3})$

Step 2

Move $4$ to the left of $π$ .

$\sin (- \frac{4 \cdot π}{3})$

Step 3

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin (\frac{2 π}{3})$

Step 4

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

$\sin (\frac{π}{3})$

Step 5

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$