Cosine Wave Simulator
Visualize y = A cos(Bx - C) + D with live graph controls
A amplitude
B frequency
C phase
D shift
Cosine Graph Formula
y = A cos(Bx - C) + D
amplitude = |A|
period = 2pi / |B|
phase shift = C / B
midline = y = D
Cosine graphs are useful for modeling oscillations that begin at a high or low point, such as seasonal cycles, rotating motion, and wave displacement.
Teaching Example: y = -3 cos(2x) + 1 has amplitude 3, period pi, midline y=1, and is reflected across the midline.
How to Read the Graph
A controls the height and reflection. B controls how quickly the cosine wave repeats. C shifts the wave horizontally. D shifts the entire graph vertically. Frequently Asked Questions
How is a cosine graph different from sine?▼
The basic cosine graph starts at a maximum when x=0, while sine starts at the midline.
What is the cosine period formula?▼
For y=A cos(Bx-C)+D, the period is 2pi divided by |B|.
What is the cosine range?▼
The range is D-|A| to D+|A|.
What does a negative A do?▼
A negative A reflects the cosine graph across its midline.
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