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Exercise #13
Writing Trigonometric Equations


The two sinusoidal equations are:

       f ( x)    a sin(b( x c)) d       OR    f ( x)   a cos(b( x c)) d
When asked to find the equation of a sinusoidal function given a graph, identify:

      a    amplitude
      b    period
      c    start point
      d    median


The following formulas may be used to identify the above variables:

           max imum min imum
       a
                   2

           max imum min imum
       d
                   2

             2
       b
           period

      c = to find the shift for sine, locate the midpoint of the period

                OR

      c = to find the shift for cosine, locate the maximum

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Exercise #13 notes ~ equations

  • 1. Exercise #13 Writing Trigonometric Equations The two sinusoidal equations are: f ( x) a sin(b( x c)) d OR f ( x) a cos(b( x c)) d When asked to find the equation of a sinusoidal function given a graph, identify: a amplitude b period c start point d median The following formulas may be used to identify the above variables: max imum min imum a 2 max imum min imum d 2 2 b period c = to find the shift for sine, locate the midpoint of the period OR c = to find the shift for cosine, locate the maximum