Sine and cosine are the same wave shifted sideways, and every parameter in the equation maps to something you can see on the graph: amplitude is height, period is width, and the rest is position. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.
Every graph in this topic is one of a small handful of parent shapes, moved. y = af(n(x − h)) + k is a single sentence — stretch it, flip it, shift it — and it reads the same whether f is a sine wave or anything else you meet. Learn to read that sentence off a picture and write it back, and modelling periodic things stops being a new topic and becomes the one you already know.
Sine and cosine graphs are horizontally shifted versions of each other where amplitude stretches vertically, period compresses or stretches horizontally, and phase shift plus vertical translation position the wave in the plane.
knowhere maps every concept to what it rests on and what rests on it — 1 underneath this one, 1 built on top. Each one says why, in a sentence, not as an arrow on a diagram.
Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.
Every HSC and VCE concept in knowhere is built like this one — mapped to your curriculum, never capped by it. Free for a week. No card tricks, no lecture.
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Free for a week, then a plan you can stop any time.
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