Phase Shift Calculator

Your details

Choose whether your function is a sine, cosine, or tangent.
The multiplier in front of the function. The amplitude of the wave equals |A|. Negative A reflects the wave vertically.
Controls how many complete cycles occur over 2pi. Period = 2pi / |B|. Must not be zero.
The horizontal-shift numerator. Phase shift = C / B. Positive C/B shifts the graph to the right.
Moves the entire wave up (positive D) or down (negative D). This is also the midline of the wave.
Enter an x-value to compute f(x) at that point. Leave at 0 to see f(0).
Display period and phase shift in radians or degrees. The coefficients A, B, C, D always use the standard radian-based formula.
Phase shiftRight shift
0.3333

Horizontal displacement: C / B (in chosen angle unit)

Amplitude2
Period2.0944
Vertical shift (midline)0
Range minimum-2
Range maximum2
f(x) at given x-1.682942
Amplitude2
Period2.0944
Phase shift0.3333

Phase shift: +0.3333 radians

  • The graph is shifted 0.3333 radians to the right relative to the base sin(x).
  • One complete cycle spans 2.0944 radians.
  • The wave oscillates between -2.0000 and 2.0000, centred on y = 0.
  • At x = 0, f(x) evaluates to -1.682942.

Next stepTo graph this function, plot the midline at y = D, mark the starting point offset by the phase shift, then repeat the pattern every one period.

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