Question

Where does the pythagorean identity sin^2 + cos^2=1 come from? How does it relate to right triangles?

Answer 1

Consider a right triangle with hypotenuse of 1.
sin x means to divide the side in front of the angle by hypotenuse
cos x means to divide the side beside  the angle by hypotenuse
we know that a^2+b^2=c^2 now divide two sides by c^2
$\frac{ a^{2} }{ c^{2} }+ \frac{ b^{2} }{ c^{2} }=1$
c is 1 also a/c means sinx and b/c is cos x so
sin^2(x)+cos^2(x)=1