Trigonometric Waves
Set the amplitude, period and phase of a sine wave yourself
Summary
Control every aspect of a sine curve with the formula y = A·sin(Bx + C) + D: A sets the amplitude (height), B the period (how squeezed or stretched it is), C the phase (horizontal shift) and D the vertical shift.
In depth
The sine and cosine functions are the universal language of periodic oscillation: sound waves, alternating current, tides, heartbeats and planetary orbits can all be broken down into sinusoidal components (the Fourier transform). This interactive visualisation lets you change the four parameters one at a time. The amplitude (A) sets how high the wave rises above its midline. The coefficient B controls the period (T = 2π/B) and the frequency (f = B/2π): as B grows, the wave is squeezed. The phase shift (C) moves the wave sideways, and the vertical shift (D) moves the whole graph up or down. With the cosine option you can see that the sine and cosine curves are the same wave, 90° (π/2 radians) apart in phase.
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