Trig ratios and functions

Question

How does the Pythagorean Theorem relate to trigonometric ratios? What is important to remember about coterminal angles and their trigonometric function values? What are some tips or tricks you would give to someone who is just starting to learn about positive and negative angles, coterminal and reference angles, and the values of trig functions?

Answer 1

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