Recall 8 trig identities.
a) sin
^{2}θ + cos
^{2}θ = 1
- derived from the Pythagorean Theorem (sin and cos are legs of a triangle while the hyp = radius (1))
b) tan
^{2}θ + 1 = sec
^{2}θ
c) 1 + cot
^{2}θ = csc
^{2}θ
d) sin(2θ) = 2(sinθ)(cosθ)
e) cos(2θ) = 1 - 2(sin
^{2}θ)
f) tan(2θ) =
g) sin(-θ) = -sin(θ) <-- odd function
h) cos(θ) = cos(-θ) <-- even function
Note: recall "odd" and "even" functions:
even: f(x) = f(-x) --> graph symm. along y-axis
odd: f(x) ≠ f(-x) --> graph symm. along its origin
instead: f(x) = -f(-x) or f(-x) = -f(x)