Unroll the Circle, Get the Wave

You'll learnto unroll a point going around the circle into the sine wave.

A point rides counterclockwise around a circle of radius 1. Carry its height out to the right as the angle grows and the sine curve draws itself; carry its across instead and you get cosine. Every feature of both parent graphs, where they start, peak, cross zero, and repeat, is already sitting on the circle waiting to be unrolled.

9 STEPS · 6 QUICK CHECKS · HEIGHT → SINE · ACROSS → COSINE · RADIANS · v3

sin θ = height · cos θ = across

Before you start

What you're looking at

A point on the unit circle whose height is carried out to the right to draw a curve.

The question

As the angle grows, what does the graph on the right record?

Watch for

The point's height, frozen at 0, π/2, π, 3π/2, 2π — sine alone for a full cycle before cosine joins.

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