Find the Exact Value sin(495 degrees )

$\sin (495 °)$

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

$\sin (135)$

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

$\sin (45)$

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.70710678 \dots$