sin^2 + cos^2 = 1 iff and only if a^2 + b^2 = c^2

Proof:

sin = a/c and cos = b/c

then (a/c)^2 + (b/c)^2 = 1

a^2/c^2 + b^2/c^2 = 1

a^2 + b^2 = c^2

The converse is proven by following the steps backwards

As far as advice goes for trig here's some helpful hints:

(1) DRAW a picture. You MUST draw a picture of the triangle in the coordinate plane

(2) REmember the following mnemonic device: All Students take Calculus or Add sugar to coffee

A: all trig functions are positive in quadrant 1

S: sine is positive in quadrant 2

T: tangent is positive in quadrant 3

C: tangent is positive in quadrant 4