A pink wave, y = sin x, on axes x and y, with x ticks π/2, π and 2π and a y tick at 1. Small gold slope bars sit on the wave: slope 1 where it starts, a flat bar marked height and slope 0 at the top, and a steep gold bar, with no number, where it crosses the axis going down at π.

At the very top the swing stops for a blink: speed is 0. In the middle it moves fastest. Height follows sine; slope follows cosine. At the top, sine is 1 and cosine is 0: highest point, zero speed.

Two waves on the same axes: a pink wave, y = sin x, and a teal wave, y = cos x, with y ticks 1 and −1 and x ticks π/2, π and 2π. At the top of the pink wave a flat gold bar sits on it, and right below, the teal wave crosses the axis.

At the start the height is 0 but the curve climbs steeply: slope 1. At the first peak the height is 1 but the curve is flat: slope 0. Height and slope are different. The teal wave is the slope of the rose wave.

A unit circle with a radius marked 1 at angle θ, a teal adjacent side marked cos θ and an amber opposite side marked sin θ. A zoom lens on the rim shows a tiny teal arc step dθ next to a tiny amber rise, with the note rise ≈ cos θ · dθ.

On the unit circle a tiny step along the arc equals the angle step, and the tiny change in height is about the adjacent side times that step, so the slope of sine is cosine. The zoom is a limit-small step, not a second full triangle.