eharetea

Anatomy of the tangent function.

Graph of tan()

Date Created:Saturday January 20th, 2007 09:06 AM
Date Modified:Saturday August 02nd, 2008 11:29 AM

ƒ(x) = tan(x)

ƒ(x) = tanθ = sinθ/cosθ, cosθ ≠ 0





properties of: ƒ(x) = tan(x)

Period	π tan(θ + π) = tanθ
Domain	All real numbers except odd multiples of nπ/2 (90°)
Range	All real numbers
Symmetry	over origin (odd function) tan(-θ) = -tanθ
Zeros	sinθ = 0 nπ; n is any integer ex: {π, 2π, 5π, etc...}
Vertical Asymptotes	cosθ = 0 nπ/2; n any odd integer ex: {-3π/2, π/2, 5π/2, etc...}

ƒ(x) = Atan(wx) + b

Amplitude	|A|
New x-axis	y=b

Quadrants

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