Answer
$$\frac{\sqrt{2}}{2}$$
Work Step by Step
To evaluate trigonometric functions without a calculator, it is necessary to use the unit circle. Doing this, we find that the function evaluates to:
$$\sin \left(405^{\circ \:}\right) \\ \sin \left(45^{\circ \:}\right) \\ \frac{\sqrt{2}}{2}$$
Note, on the unit circle 45 and 405 degrees are at the same location.
