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

f (x) = A \sin (c x + 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 $ϕ = - c \cdot u$ .

Theory

Cosine Function

f (x) = A \cos (c x + ϕ) + d

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

These formulas for the rest of the coefficients apply to both the sine and cosine functions:

\begin{array}{l} d & = \frac{y_{\max} + y_{\min}}{2} \\ A & = \frac{y_{\max} - y_{\min}}{2} \\ c & = \frac{2 π}{P} \end{array}

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