The fact that it's a fixed point comes from the triplke angle formula just a few lines above. Substitute and simplify, and you'll see that f applied to sin(1 de

The fact that it's a fixed point comes from the triplke angle formula just a few lines above. Substitute and simplify, and you'll see that f applied to sin(1 deg) returns sin(1 deg). As to why it conveges when iterated, starting from a value that's close enough, that's a different question. Is that what you actually intended to ask?