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Write the equation of a sinusoidal function

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Useful for: MCR3U MCF3M IB Math AA SL & HL AP® Precalculus

Learn it From a description: a = (max − min)/2, c = (max + min)/2, k = 360°/period. For a cosine model, the phase shift d is where the first maximum occurs.

Example: Max 9 at x = 20°, min 1, period 120°. Write a cosine equation.

  1. a = 4, c = 5, k = 360/120 = 3, d = 20.
  2. y = 4 cos[3(x − 20°)] + 5.

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