The Math Meridian
Back to Periodic and Sinusoidal Functions

Transformations: amplitude, period, phase shift and axis

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

Learn it In y = a sin[k(x − d)] + c: amplitude |a|, period 360°/|k| (or 2π/|k|), phase shift d (right if positive), axis y = c. Max = c + |a|, min = c − |a|.

Example: y = 3 sin[2(x − 30°)] + 5.

  1. Amplitude 3, period 360°/2 = 180°.
  2. Phase shift 30° right, axis y = 5, max 8, min 2.

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