Hi, I just learn about Pythagorean identities.
As i know that cos^2θ + sin^2θ = 1
but what is the work out to get 1? and why 1?
Thanks.
Consider a right triangle like here, i.e., the hypothenuse is denoted by h, opposite side is a and adjacent side is b.
Then:
sinθ=a/h
cosθ=b/h
and you know from Pythagorean theorem that .
So if you calculate , you get
You can even simplify this by rescaling the triangle so that h=1. (In case you're familiar with unit circle definitions of trigonometric functions, you should know, what I mean.)
BTW you have a whole article about this identity at wikipedia.