Find the Exact Value sin(480 degrees )

$\sin (480 °)$

Step 1

Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$\sin (120)$

Step 2

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

$\sin (60)$

Step 3

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$