Using a diagram of the Unit Circle, centre (0,0) and radius equal to 1 unit,

the vertical co-ordinate of a point on the circumference is the Sine of the angle.

When the angle is zero, the vertical co-ordinate is zero.

When the angle is 90 degrees, the vertical co-ordinate is 1.

When the angle is 180 degrees, the vertical co-ordinate is 0.

When the angle is 270 degrees, the vertical co-ordinate is -1.

Another 90 degrees on and we are back where we started.

Hence any multiple of 360 degrees added to the angle gives us the same vertical co-ordinate.

Knowing the periodicity allows you to determine the Sine of your given angle

by subtracting 360 degrees twice.