The periods of the trigonometric functions sine and cosine are both 2 times pi. The functions tangent and cotangent both have a period of pi. The general formula for the period of a trigonometric function can be determined by dividing the regular period by the absolute value of any multipliers.
The period of a function is the length of each unique wave. For example, the sine and cosine repeat every 360 degrees, which is equal to two pi in radians. The period of the function sin(2X) repeats every 180 degrees, or pi radians, giving that function a period of pi by dividing the regular sine period of 2 pi by the multiplier, 2, in the equation.