I remember playing around with these weird sin and cos functions whose return values seemed to lack any readily discernible pattern. After some experimenting I ended up plotting something like

  x=a*sin(t)
  y=a*cos(t)

and was delighted to realize that the coordinates traced the arc of a circle! Not a long time earlier I had wondered how to write a program that displays an analog clock… The connection to right-angled triangles was revealed to me only later, although in retrospect they are obviously two sides of the same coin.