Sine, cosine and tangent are the graphs you get by reading the unit circle as an angle grows, and every letter in y = a sin(n(x − h)) + k is a move you can point to on the picture: |a| is the height from the midline to a peak, 2π/n is the width of one full wave, h slides the wave sideways and k lifts its midline to y = k. Cosine is the same wave as sine starting π/2 earlier, so cos x = sin(x + π/2). Tangent is different in kind: it has no amplitude, climbs from −∞ to +∞ between vertical asymptotes where cos = 0, and repeats every π rather than every 2π. 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.
A labelled graph on −2π ≤ x ≤ 2π that switches between sin, cos and tan while a, n, h and k change the drawn curve: a dashed bracket measures one period from the curve, dashed lines mark the midline, the amplitude envelope and tan's asymptotes, and amber dots mark the intercepts.
knowhere maps every concept to what it rests on and what rests on it — 4 underneath this one, 4 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.
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