What is the Secant Function?
The secant function (sec) is one of the six fundamental trigonometric functions. It is defined as the reciprocal of the cosine function: sec(θ) = 1/cos(θ). The secant function relates to the ratio of the hypotenuse to the adjacent side in a right triangle.
Key Properties
Definition
Secant is the reciprocal of cosine.
sec(θ) = 1 / cos(θ)
Domain
sec(θ) is undefined where cos(θ) = 0, i.e., at θ = 90° + 180°n.
θ ≠ 90° + 180°n
Range
The secant function outputs values in (-infinity, -1] and [1, infinity).
|sec(θ)| ≥ 1
Period
The secant function has a period of 360° (2π radians).
sec(θ + 360°) = sec(θ)
Common Secant Values
- sec(0°) = 1
- sec(30°) = 2/√3 ≈ 1.1547
- sec(45°) = √2 ≈ 1.4142
- sec(60°) = 2
- sec(90°) = undefined
- sec(180°) = -1
Secant Identity
The secant function is related to other trig functions through several identities:
- sec2(θ) = 1 + tan2(θ)
- sec(-θ) = sec(θ) (even function)
- sec(π - θ) = -sec(θ)