Sec(x)
Sec(x)Tan(x)
The secant function, denoted as sec(x), is a trigonometric function that represents the reciprocal of the cosine function for an angle x. It is defined as follows:
sec(x) = 1/cos(x)
The secant function has a periodicity of 2π and it is an even function, which means that sec(-x) = sec(x). The domain of the secant function is all real numbers except for the values where cos(x) = 0, which results in undefined values.
The graph of sec(x) is similar to the graph of cos(x), but it has vertical asymptotes at x = (2n + 1)π/2, where n is any integer. These asymptotes occur where the cosine function is equal to zero.
Some important properties of the secant function include:
– The range of sec(x) is (-∞, -1] ∪ [1, ∞).
– The secant function is continuous and smooth throughout its domain.
– The secant function is not periodic, but it has a basic period of 2π.
– The secant function is important in many mathematical applications, including calculus, engineering, and physics.
Overall, the secant function is an important trigonometric function that represents the reciprocal of the cosine function and has several important properties and applications.
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