Caveat: This is NOT meant to be a rigorous explanation of QAM. You can read a book like Telecommunication Breakdown or Principles of Communications by Ziemer and Tranter for such explanations(of course, Wikipedia also works at times). These three plots are just meant to build intuition.

Note: Message signals in general are NOT sinusoids! (sin(x) or cos(x))

Enjoy. Click on the thumbnails to enlarge the graphs. Of course, there is no noise effect and no demodulator plots shown here.

First step: y = sin(x)*sin(50x)

Second step: y = cos(x)*cos(50x)

Third step: y = sin(x)*sin(50x) + cos(x)*cos(50x)

A quick way to make screencaptures is to press Apple-Shift-3(the screenshot will be put on the Desktop)