eharetea

Anatomy of the cotangent function.

Graph of cot()

Date Created:Saturday January 20th, 2007 09:06 AM
Date Modified:Saturday August 02nd, 2008 11:36 AM

ƒ(x) = cot(x)

ƒ(x) = cotθ = cosθ/sinθ, sinθ ≠ 0





properties of: ƒ(x) = cot(x)

Period	π cot(θ + π) = cotθ
Domain	All real numbers except multiples of π (180°)
Range	All real numbers
Symmetry	over origin (odd function) cot(-θ) = -cotθ
Zeros	cosθ = 0 nπ/2; n any odd integer ex: {-3π/2, π/2, 5π/2, etc...}
Vertical Asymptotes	sinθ = 0 nπ; n is any integer ex: {π, 2π, 5π, etc...}

ƒ(x) = Acot(wx) + b

Amplitude	|A|
New x-axis	y=b

Quadrants

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