Sine/Cosine Wave Explorer

Sine and cosine aren't really about triangles — they're the horizontal and vertical shadow of a point moving at constant speed around a circle. As the point sweeps through angle θ = Bx + C, its vertical position traces sin(θ) while its horizontal position traces cos(θ), which is exactly why the two curves are identical except for a quarter-turn (π/2) phase offset. This is also why B controls frequency but never amplitude: B only changes how fast the point goes around the wheel, not how far its shadow swings. The same rotating-vector idea — a spinning wheel in disguise — is how engineers describe AC electricity, sound, and radio signals as phasors.

Every wave here is the same basic S-shape, reshaped by just four numbers. A stretches it taller, B squeezes it sideways to fit more cycles into the same space, C slides it left or right, and D lifts or lowers the whole thing. The one thing worth remembering: only B changes the period (how long one full cycle takes). No matter how you set A, C, or D, the wave still repeats over exactly the same length — its rhythm stays untouched.

The word sine is an accident of history. Indian mathematicians called it jyā (bowstring); Arabic scholars borrowed it as jayb, which also happened to mean 'bay' or 'fold'. When Latin translators read the word, they rendered that unrelated meaning literally as sinus — Latin for a bay or the fold of a garment. So every time you write sin, you are using a 12th-century mistranslation of 'bowstring' into 'fold'.