## Periodic function

A function  is said to be periodic if it satisfies with constant value

 (2-1)

The least such positive value  for which (2-1) holds is called the period of . Given the period  of , we have for any integer ,

 (2-2)

Period. The sine function and the cosine function are periodic, and both have the period of . That is,

 and (2-3)

(2-2) and (2-3) together implies that we have for any integer ,

and

Phase shift. The constant value  is not the period for the sine and the cosine functions, but gives the following formulas of phase shift:

and

Values of sine and cosine functions. Use the reference angle '' (the acute angle between the terminal side of the original angle  and the -axis) to find the coordinate  on the unit circle.

Department of Mathematics