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