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Home›Function Tools›Trig Function Curve Fitter

Trig Function Curve Fitter

Compute sine wave parameters: y = a*sin(bx+c) + d

Input Sine Wave Parameters

y =*sin(x +) +

Sine Wave Parameters

y = a*sin(bx + c) + d

Amplitude = |a|, Period = 2pi/|b|

Phase shift = -c/b (horizontal shift)

Midline = d (vertical shift)

Sine wave parameters describe the shape and position of a sinusoidal curve. Amplitude controls height, frequency controls cycles per unit, phase shift moves the wave horizontally, and vertical shift moves the center line.

⚠ For fitting from data points: a=(max-min)/2, d=(max+min)/2, T=distance between peaks, b=2pi/T.

What Is Sine Curve Fitting?

Sine curve fitting determines the four parameters of y=a*sin(bx+c)+d from data or known properties. The amplitude and vertical shift come from max/min values. The period determines frequency. The phase shift aligns the wave with data points.

Amplitude a

|a| = half the vertical range. Determines the height of oscillations from the midline.

Angular Frequency b

b = 2pi/T. Larger b means more oscillations per unit. b=1 gives period 2pi.

Phase Shift -c/b

Horizontal shift of the wave. Positive shift moves right. Negative moves left.

Vertical Shift d

Moves the midline up/down. Range = [d-|a|, d+|a|]. y = sin(x)+1 oscillates between 0 and 2.

Teaching Example: y=3*sin(2x+1)-1. amp=3, period=2pi/2=pi, phase=-1/2=-0.5, midline=-1. Range=[-4,2]. Zeros: 2x+1=n*pi -> x=(n*pi-1)/2.

Applications

Signal Processing Wave Analysis Physics Audio Electronics

Frequently Asked Questions

Sine wave parameters?▼

y=a*sin(bx+c)+d. a=amplitude, b=2pi/period, c/b=phase shift, d=midline.

Find amplitude from data?▼

a=(max-min)/2. Half the distance between highest and lowest points of the wave.

Period from b?▼

T=2pi/|b|. b=2 gives T=pi, b=0.5 gives T=4pi. Frequency inversely related to period.

Phase shift meaning?▼

-c/b is horizontal translation. sin(x+pi/2)=cos(x): shifts left by pi/2.

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