Sine Wave Simulator
Adjust amplitude, period, phase shift, and midline
Sine Wave Formulas
| General form | y = A sin(Bx + C) + D |
| Amplitude | |A| |
| Period | 2pi / |B| |
| Phase shift | -C / B |
Step-by-Step Example
For y = 3 sin(2x - 1) + 4, the amplitude is 3, the period is 2pi / 2 = pi, the phase shift is -(-1)/2 = 0.5, and the midline is y = 4.
Common Mistakes
- Using B as the period. The period is 2pi / |B|.
- Forgetting the negative sign in the phase shift formula.
- Confusing vertical shift with amplitude.
Frequently Asked Questions
What is the sine wave formula?▼
A common sine wave form is y = A sin(Bx + C) + D, where A is amplitude, B affects period, C affects phase shift, and D shifts the midline.
How do you calculate period?▼
For y = A sin(Bx + C) + D, the period is 2pi divided by the absolute value of B.
What is amplitude?▼
Amplitude is the distance from the midline to a peak or trough. It equals the absolute value of A.
What is phase shift?▼
Phase shift is the horizontal shift of the wave. For A sin(Bx + C) + D, it is -C/B.
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