Periodic functions > More trigonometric graphs
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## Theory

When a periodical phenomenon can be described by a sinusoid, you can find the corresponding function by determining:

• the equilibrium $y=d$;

• the amplitude $a$(maximum deviation from the equlibrium);

• the period $p$;

• the horizontal translation (w.r.t. the standard graph) $c$.

Two function rules are possible:

• $f\left(x\right)=asin\left(b\left(x-{c}_{1}\right)\right)+d$ where $b=\frac{2\pi }{p}$

• $f\left(x\right)=acos\left(b\left(x-{c}_{2}\right)\right)+d$ where $b=\frac{2\pi }{p}$

Note that the values for $a$, $b$ and $d$ are the same for both, but that the values of $c$ are not. The translation with respect to the standard sine is different from the one with respect to the standard cosine.