eharetea

Anatomy of a cosine wave.

Trigonometric cosine wave.

Date Created:Saturday January 20th, 2007 09:06 AM
Date Modified:Saturday August 02nd, 2008 11:27 AM

SOHCAHTOA
cosθ = adjacent/hypotneuse

ƒ(x) = cos(x)

if evaluating on a circle of radius r, ƒ(θ) = cosθ = x/r

ƒ(x)	x
0	1
π/2	0
π	-1
3π/2	0
2π	1

properties of: ƒ(x) = cos(x)

Period	2π cos(θ + 2π) = cosθ
Domain	All real numbers
Range	[-1,1]
Symmetry	over y-axis (even function) cos(-θ) = cosθ
Zeros	nπ/2; n is an odd integer ex: {π/2, 3π/2, 5π/2, etc...} (90°)

ƒ(x) = Acos(wx) + b

Period	2π/w
Amplitude	|A|
new x-axis	y=b

sinθ = cos(θ-π/2)
cosθ = sin(θ+π/2)

Quadrants

QII (-,+) - = negative	QI (+,+) + = positive
QIII (-,-) - = negative	QIV (+,-) + = positive