Pythagorean Theorem for Sines and Cosines

It's time to look at one of the most fundamental identities in trig:
I can't count the number of times I've used that identity. I can however, count the number of times I've used it since I knew why it was true. This proof will be a breeze after the SOHCAHTOA work. We'll use the unit circle again for this proof:

• To start with, we need to remember that with regards to right triangles when is the hypotenuse,

• Referring to the unit circle above, and specifically , we can say that and

• This means that

• So, using the Pythagorean Theorem, we can say that

• Giving us the end result