The sec function, the reciprocal of the cosine function, has several important properties that are useful in trigonometric analysis and applications. Here are some of its key properties:
1)Periodicity: The sec function is periodic with a period of 2π, which means it repeats its value every 2π units. This is expressed as sec(θ+2π) = sec(θ) for any angle θ.
2)Domain: The domain of the sec function includes all real numbers except odd multiples of π/2, where sec(θ) would be undefined due to division by zero. Thus, θ ≠ ±π/2, ±3π/2, ±5π/2,...
3)Range: The range of the sec function is less than or equal to -1, or greater than or equal to 1. Thus, sec(θ) ≤ -1 or sec(θ) ≥ 1.
4)Symmetry: The sec function is an even function, which means that sec(-θ) = sec(θ). This property indicates that the sec function is symmetric about the y-axis.
5)Asymptotes: The sec function has vertical asymptotes at odd multiples of π/2. This means that sec(θ) is undefined at θ = π/2 ± nπ for integers.