Cosine and sine are not new functions to memorise — they are just the two coordinates of a point going round a circle. Drag it, or press play.
WAVE
θ=45°=π/4
(cos θ, sin θ) =0.707,0.707
THE CIRCLE — DRAG THE POINTy = sin(x)(0.79, 0.71)
The height of the point on the circle is sin θ, and its horizontal position is cos θ. Press play and watch the blue bar on the left trace out the wave on the right.