Practice Periodic Functions in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A periodic function repeats its values at regular intervals: f(x + T) = f(x) for all x, where T > 0 is the period — the length of one complete cycle.
The same pattern over and over. Like a heartbeat or the seasons.
Example 1
easyVerify that f(x) = \sin(x) is periodic with period 2\pi by checking the definition f(x + p) = f(x).
Example 2
mediumFind the period of g(x) = \cos(3x) and sketch one complete cycle.
Example 3
easyThe function h(x) = \tan(x) has period \pi. What is \tan\!\left(\frac{5\pi}{4}\right) given that \tan\!\left(\frac{\pi}{4}\right) = 1?
Example 4
hardA function satisfies f(x+4) = f(x) for all x, and is defined on [0,4) by f(x) = x^2 - 4x + 3. Find f(13.5).