Cos^2 + Sin^2 = 1

I know that this is just the Pythagorean Theorem, so here we are saying that the radius of the circle is 1? As cos = x ( base) and sin = y ( height ), what happens if the circle's radius is 5. Does this apply only to the unit circle? How can the hypotenuse always be 1?

(x-1)^2 + ( y+2)^2 = 3^2

So again it applies but for a circle at x= 1 and y= -2. So, how does that equation equal 9? Isn't that 1+4=3^2. Please help!