How can you prove that sine and cosine correspond to side lengths of right triangles, without using identities?

Answer 1

A triangle is labeled "a" short side; "b"mid; "c" longest (hypotenuse).

"alpha" is the corner opposite "a". "beta" b; "gamma" c.

So: a/(sin(alpha))=b/(sin(beta))=c/(sin(gamma)).

((cos)(alpha))=a/c=((sin)(beta)); ((cos)(beta))=b/c=((sin)(alpha))