25.4.1 The Birth of the Sine Curve
Core ideaLet the point on the unit circle turn with the angle and trace its height point by point, and those points join into a rolling sine wave.
Module goal. We 'unroll' the turning of a point on the unit circle into a wavy curve, getting a firm grip on period, even/odd symmetry, increasing/decreasing behavior, and extremes, to lay the groundwork for parameter transformations and the laws of sines and cosines.