Interactive sine wave grapher. Visualize y = A·sin(Bx + C) + D with real-time adjustments for amplitude, period, phase shift, and vertical shift.
Controls the height of the wave (max = A, min = -A). Limited to ±2 to fit graph bounds.
Controls how quickly the wave repeats (1 = standard 2π period)
Shifts the wave left (positive C) or right (negative C)
Moves the entire wave up (positive D) or down (negative D). Limited to ±2 to fit graph bounds.
The sine function is one of the fundamental trigonometric functions, representing the y-coordinate of a point on the unit circle.
Odd Function: sin(-x) = -sin(x), meaning the graph is symmetric about the origin.
Stretches or compresses vertically. |A| is the distance from midline to peak.
If A < 0, the graph is reflected over the x-axis.
B > 1 compresses horizontally (shorter period)
0 < B < 1 stretches horizontally (longer period)
Shifts the graph horizontally. Positive C shifts left, negative C shifts right.
Moves the entire graph up (D > 0) or down (D < 0).
The cosine graph is the same as the sine graph shifted left by π/2. Mathematically: cos(x) = sin(x + π/2). Both have the same shape, amplitude, and period, just different starting points.
1) Find amplitude: (max - min) / 2 = A
2) Find vertical shift: (max + min) / 2 = D
3) Find period: distance between two maximums, then B = 2π/period
4) Find phase shift: where the first "standard" sine pattern begins
Sine waves model periodic phenomena in nature: sound waves, light waves, ocean tides, AC electricity, pendulum motion, and more. They're fundamental in physics, engineering, signal processing, and music.