eharetea

Anatomy of the cosecant function.

Graph of csc()

Date Created:Saturday January 20th, 2007 09:06 AM
Date Modified:Saturday August 02nd, 2008 11:41 AM

ƒ(x) = csc(x)

ƒ(x) = cscθ = 1/sinθ, sinθ ≠ 0

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



properties of: ƒ(x) = csc(x)

Period	2π csc(θ + 2π) = cscθ
Range	y≤-1 or y≥1 absolute notation: |cscθ| ≥ 1 or 1/|sinθ| ≥ 1
Domain	All real numbers except multiples of nπ (180°)
Symmetry	over origin (odd function) csc(-θ) = -cscθ
Zeros	no x-intercepts
Vertical Asymptotes	sinθ = 0 nπ; n is any integer ex: {π, 2π, 5π, etc...}

ƒ(x) = Acsc(wx) + b

Amplitude	|A|
New x-axis	y=b

Quadrants

QII (-,+) 1/+ = positive	QI (+,+) 1/+ = positive
QIII (-,-) 1/- = negative	QIV (+,-) 1/- = negative

Sine and Cosecant are related: