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Inverse secant calculator

This tool evaluates the inverse secant of a number: arcsec(x). The principal branch is evaluated, where the return values range between 0 and π.

x =
Result:
arcsec(x) =		deg rad

Definitions

General

The inverse secant function, in modern notation written as arcsec(x), gives the angle θ, so that:

Due to the periodical nature of the secant function, there are many angles θ that can give the same secant value (i.e. θ+2π, θ+4π, etc.). As a result, it is impossible to define a single inverse function, unless the range of the return values is restricted, so that a one-to-one relationship between θ and secθ can be established. Therefore, multiple branches of the arcsec function can be defined. Commonly, the desired range of θ values spans between 0 and π. The branch of arcsec, in that case, is called the principal branch.

Series

The arcsec function can be defined in a Taylor series form, like this:

The above series is valid for |x|≥1.

Properties

The derivative of the arcsec function is:

The integral of the arcsec function is given by:

The following properties are also valid for the arcsec function: