Divide by zero, funny behavior. With a white/black input it won’t show well.
The sine output shown here isn’t that useful either.
There aren’t really many surprises with math nodes if you know what you’re giving them. The 1-x node literally subtracts the input from 1. Sin/cosine nodes have a ‘period’ that you may want to experiment with, as I think the default is meant for radians. Color is typically in a 0 to 1 range, not a 0 to 255 range, so multiplying usually gives you a darker result rather than a very large/bright one. Emissive values above 1 can be brighter than specular highlights, but most other material outputs will clamp to the 0 to 1 range (which is a shame).
Some other nodes to keep a reference of: Clamp, lerp (a favorite), componentmask, max/min, and if.
Simplistic Scenerio for the “If” node. Would be say, you wish to replace colors within “bands”, simplest would be of course White/Black and turning that into say Orange/White output. Especialy when driven by TextureParameters, allowing the White/Black to be changed very easily with the Orange/White. Set the compare value to 0.05 (or threshold, however you wish to think of it), one could also create an infinite number of bands in this fashion, simply by cascading them.