Because the angle is rotating around and around the circle the Sine, Cosine and Tangent functions repeat once every full rotation (see Amplitude, Period, Phase Shift and Frequency).
When we want to calculate the function for an angle larger than a full rotation of 360° (2π radians) we subtract as many full rotations as needed to bring it back below 360° (2π radians):
Example: what is the cosine of 370°?
370° is greater than 360° so let us subtract 360°
370° − 360° = 10°
cos(370°) = cos(10°) = 0.985 (to 3 decimal places)
And when the angle is less than zero, just add full rotations.
Example: what is the sine of −3 radians?
−3 is less than 0 so let us add 2π radians
−3 + 2π = −3 + 6.283… = 3.283… radians
sin(−3) = sin(3.283…) = −0.141 (to 3 decimal places)
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