eharetea

Anatomy of the secant function.

Graph of sec()

Date Created:Saturday January 20th, 2007 09:06 AM
Date Modified:Saturday August 02nd, 2008 11:38 AM

ƒ(x) = sec(x)

ƒ(x) = secθ = 1/cosθ, cosθ ≠ 0

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






properties of: ƒ(x) = sec(x)

Period	2π sec(θ + 2π) = secθ
Range	y≤-1 or y≥1
Domain	All real numbers except odd multiples of nπ/2 (180°)
Symmetry	over y-axis (even function) sec(-θ) = secθ
Zeros	no x-intercepts
Vertical Asymptotes	cosθ = 0 nπ/2; n any odd integer ex: {-3π/2, π/2, 5π/2, etc...}

ƒ(x) = Asec(wx) + b

Amplitude	|A|
New x-axis	y=b

Quadrants

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

Cosine and Secant are related: