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 ( x ) = a sin ( b ( x c 1 ) ) + d where b = 2 π p

  • f ( x ) = a cos ( b ( x c 2 ) ) + d where b = 2 π 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.

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