Consider the core trigonometric functions: sine and cosine.

This is apparent by reviewing the mapping diagrams along with the graphs in our initial examples for this section.

But first we review the key concept for periodic behavior for a function.In the following theorem, graphs and mapping diagrams visualize the facts that the sine and cosine functions have period

You can use this next dynamic example to investigate visually the period effects of composition of the sine and cosine functions with the core linear functions $f_m(x)=mx$ on a mapping diagram of these functions and their connection to the wrapping function.

See also TRIG.APP Trigonometric Function Applications on the amplitude, period, and phase shift of wave functions.