The circle clock
x never moves. y rotates clockwise: theta = 0.00 radians.
x · y = 1.000
cos(theta) = x · y||x|| ||y|| = 1.000
Cosine similarity
is a clock.
Keep x pointing straight up. Let y walk around the circle one tick at a time. The dot product is the height of y, which is exactly the cosine value on the curve.
The cosine curve
The moving dot has the same horizontal position theta and vertical position cos(theta) as the clock's dot product.
The slider controls k. Each tick changes theta by 2 pi / K, with K = 64. Try pausing at the top, side, and bottom of the clock.