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What Are Trigonometric Models?

A trigonometric model is used when the data seems to follow a cyclical pattern, repeating over time. Examples of this are the height of the sun in the sky, or changes in temperature over the course of a day. When you want to model your data with trigonometric functions, use one of the formulas below.

Theory

Sine Function

Trigonometric model of the sine function

Trigonometric model of the sine function

f(x) = A sin(cx + ϕ) + d

Let u be the x-value where the graph rises past the equilibrium for the first time after passing the second (y) axis. This means that ϕ = c u.

Theory

Cosine Function

Trigonometric model of the cosine function

Trigonometric model of the cosine function

f(x) = A cos(cx + ϕ) + d

Let u be the x-value of the first maximum to the right of the second (y) axis. In this case, ϕ = c u.

These formulas for the rest of the coefficients apply to both the sine and cosine functions: d = ymax + ymin 2 A = ymax ymin 2 c = 2π P

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