ForumGeneral Discussion ► Today I Learned <something scientific/historical/academic or just pretty cool>... [Not a Status-update Thread]
The coolest thing about sin2 + cos2 = 1 is less that it's a super important trig identity, it's kinda the trig identity. I'm sure there's some more abstract and arbitrary definition but that's the one I would use to define the functions sin and cos.

That said I'm a dirty physicist and mathematicians always scoff at our proofs and definitions.
  
Yeah, let me tell you, sin2 + cos2 =1 has saved my ass in a couple tests, because it’s the easiest Pythagorean trig thingy to remember AND the basis for the other two Pythagorean things.
  
Everything in math is always so weirdly interconnected. Sometimes I'll be working on a homework assignment and I'll literally mutter to myself "I swear to god, if this turns out to be the Fibonacci sequence or the golden ratio...". And it usually does.
  
Forum > General Discussion > Today I Learned <something scientific/historical/academic or just pretty cool>... [Not a Status-update Thread]