Sine Wave Simulator
Adjust y = A sin(Bx - C) + D and watch the graph update
A amplitude
B frequency
C phase
D shift
Sine Graph Formula
y = A sin(Bx - C) + D
amplitude = |A|
period = 2pi / |B|
phase shift = C / B
midline = y = D
A sine wave is periodic and repeats every period. This simulator helps connect each parameter to a visible graph transformation.
Teaching Example: y = 2 sin(3x - 1) + 0.5 has amplitude 2, period 2pi/3, phase shift 1/3, and midline y=0.5.
How to Use This Simulator
Increase A to stretch the wave vertically.
Increase B to shorten the period and make the wave repeat faster.
Change C to move the graph left or right.
Change D to move the midline up or down.
Frequently Asked Questions
What does amplitude do in a sine graph?▼
Amplitude is the distance from the midline to a maximum or minimum. In y=A sin(Bx-C)+D, it is |A|.
How do you find the period?▼
For y=A sin(Bx-C)+D, the period is 2pi divided by |B|.
What is phase shift?▼
Phase shift is C/B, the horizontal movement of the sine wave.
What is the midline?▼
The midline is y=D, the horizontal center line of the wave.
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