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Wize High School Grade 11 Math Textbook > Sinusoidal Functions (degrees)

Periodic and Sinusoidal Functions

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Periodic Functions

A periodic function is any function that repeats over and over again at a regular interval.

The period is the length or duration of one repeating cycle (measured on the xx-axis).


  • Periodic functions have peaks/crests (maximum points) and troughs (minimum points).
  • We can find the equation of the axis by taking the average of the max and min y-values:
y=max value + min value2\boxed{y=\dfrac{\text{max value + min value}}{2}}
  • The amplitude is the vertical distance from the max (or min) to the axis. We can calculate it using the formula:
y=max value−min value2\boxed{y=\dfrac{\text{max value} - \text{min value}}{2}}

Practice: Periodic Functions

Select all of the following graphs and tables of values that represent periodic functions.