Graphs of trigonometric functions
A trigonometric function like sine or cosine graphs as a repeating wave, and you can choose specific amplitude (wave height), frequency (how often it repeats), and midline (its center line) to model a real repeating pattern: a tide rising 3 feet above and below a midline of 5 feet, completing one full cycle every 12 hours, can be modeled as h(t) = 3 sin((2*pi/12)t) + 5. At t=3 hours, a quarter of the way through the cycle, h(3) = 3 sin(pi/2) + 5 = 3(1) + 5 = 8 feet, the tide's peak height.
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