Geometry help?

Pythagorean Theorem:
a^2 + b^2 = c^2
a = opposite; b = adjacent; c = hypothenuse

Pythagorean Theorem: a^2 + b^2 = c^2
Divide all of them by c^2: a^2/c^2 + b^2/c^2 = c^2/c^2
This results in: a^2/c^2 + b^2/c^2 = 1
Simplify: (a/c)^2 + (b/c)^2 = 1
Write in terms of sides:
(opposite/hypothenuse)^2 + (adjacent/hypothenuse)^2 = 1

We know the following:
sin(A) = opposite/hypothenuse
cos(A) = adjacent/hypothenuse

So we can replace those values with the appropriate trig functions
[sin(A)]^2 + [cos(A)]^2 = 1

Hope this helps!

If you go back to the right triangle, where x^2 + y^2 = r^2 (using Pythagoras)

sin = y/r --> sin^2 = y^2 / r^2
cos = x/r --> cos^2 = x^2 / r^2

sin^2 + cos^2 = y^2 / r^2 + x^2 / r^2 =
(y^2 + x^2)/r^2
but y^2 + x^2 = r^2, so this becomes r^2 / r^2 = 1

This is probably THE most important trig identity to know...

that is a trigometric function