Find amplitude, period, phase shift, and midline of a cosine graph
Result
Cosine Graph Features
Step-by-Step Derivation
Cosine Graph Formula
y = A cos(Bx + C) + D
The standard cosine graph form describes the major transformations of the wave. The coefficients determine vertical stretch, period, horizontal shift, and midline.
⚠B must not be zero. Period is reported in radians for the standard graph equation.
How Cosine Graph Analysis Works
A cosine graph repeats like a sine graph but starts at a maximum in its parent form. The same transformation rules apply to A, B, C, and D.
Amplitude
Amplitude is |A|.
Period
Period is 2π/|B|.
Phase Shift
Phase shift is -C/B.
Midline
Midline is y=D.
💡 Example: For y=-3cos(2x+4)-1, amplitude=3, period=π, phase shift=-2, midline y=-1.
Applications of Cosine Graphs
Wave ModelingRotationsSeasonal DataTrig Graphing
Frequently Asked Questions
What is a cosine graph calculator?▼
It finds key graph features of y = A cos(Bx + C) + D.
What does it calculate?▼
It calculates amplitude, period, phase shift, and midline.
How do I use this calculator?▼
Enter A, B, C, and D from the cosine function, then click Calculate.
What is the cosine period formula?▼
The period is 2π/|B|.
Where are cosine graphs used?▼
They are used for waves, rotations, oscillations, seasonal data, and trigonometry graphing.
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