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Sinusoidal Phase-Shift Calculator — result sheet
Analyze a transformed sine or cosine function to find amplitude, period, horizontal phase shift, midline, and the value at a chosen x-coordinate.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: y = A sin(Bx − C) + D or y = A cos(Bx − C) + D; amplitude = |A|, period = 2π/B, phase shift = C/B, and midline = D.
The coefficients describe the same transformation pattern used in trigonometric graphing: A controls vertical stretch and reflection, B controls period, C/B is the horizontal displacement, and D moves the midline.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Waveform — 2 choices
- Amplitude coefficient A — minimum -1000000; maximum 1000000
- Frequency coefficient B — minimum 1.0E-6; maximum 1000000
- Phase coefficient C — minimum -1000000; maximum 1000000
- Vertical shift D — minimum -1000000; maximum 1000000
- Evaluate at x — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Waveform | sine |
| Amplitude coefficient A | 3 |
| Frequency coefficient B | 1.5707963267949 |
| Phase coefficient C | 0.78539816339745 |
| Vertical shift D | 2 |
| Evaluate at x | 1 |
Amplitude = 3; period = 4; phase shift = 0.5 units right; midline y = 2; y(1) ≈ 4.12132.
Assumptions and limits
- The frequency coefficient B is positive, so the reported period is 2π/B.
- The phase shift is expressed in the same x-units used by the input and is positive to the right in the form B(x−C/B).
- The evaluation uses radians inside sine or cosine; x may represent time, distance, angle, or another modeled variable.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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