Mastering The Arctan Function: Definition, Properties, And Examples Of Inverse Tangent Function

arctan(x)

1/(1+x^2)

The function arctan(x), also known as the inverse tangent function or the arc tangent function, is the inverse of the tangent function. It is defined as follows:

arctan(x) = y, where tan(y) = x and y is in the interval [-π/2, π/2]

In other words, the arctan function takes an input x which is a real number and returns an output y which is the angle whose tangent is x.

Some important things to know about arctan(x) are:

– It returns an angle in radians.
– It is a periodic function with a period of π.
– Its range is the open interval (-π/2, π/2).

For example, if we want to find the value of arctan(1), we need to find the angle whose tangent is 1. This angle is π/4 radians (45 degrees). Therefore, arctan(1) = π/4.

Similarly, if we want to find the value of arctan(0), we need to find the angle whose tangent is 0. This angle is 0 radians (0 degrees). Therefore, arctan(0) = 0.

Note that arctan(x) is not defined for x outside the open interval (-∞, ∞).

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