Phase Shift Calculator
MathFind the amplitude, period, phase shift, and vertical shift of a sinusoidal function A*sin(Bx - C) + D.
Amplitude
How far the function swings above and below its midline, |A|.
Period
3.1416
The length of one full cycle, 2*pi / |B|.
Phase Shift
1.5000
The horizontal shift of the wave, C / B. Positive means shifted right.
Vertical Shift
4.0000
How far the function's midline sits above or below the x-axis, D.
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Frequently Asked Questions
What does phase shift mean?
Phase shift is how far a sine or cosine wave is shifted left or right compared to the plain, unshifted version of the function. In f(x) = A*sin(Bx - C) + D, the phase shift is C/B.
Why divide C by B for the phase shift?
The function's argument is Bx - C, which factors as B(x - C/B). This shows the wave is exactly the shape of sin(Bx), just shifted so its zero crossing moves to x = C/B instead of x = 0.
What is the difference between phase shift and vertical shift?
Phase shift moves the wave left or right (horizontally), changing when each part of the cycle happens. Vertical shift moves the entire wave up or down, changing its baseline value without affecting timing.
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