The sine and cosine curves themselves are shown for reference, and all four possible combinations of sine and/or cosine which nest one function inside another (with values for the outer function to evaluate ranging from -2π to 2π) are also shown.
To make the virtual “painting” above, I plotted simple and moderately-complex trigonometric functions on a single coordinate plane, as shown below, using Geometer’s Sketchpad. I then erased all the text, etc., copied-and-pasted a screenshot into MS-Paint, and used that program to make the finished image above.
The last post made me curious about other trigonometric functions’ graphs, in a polar coordinate system. They were not what I expected. Here they are.