y = arctanx
The equation y = arctan(x) represents the inverse tangent function
The equation y = arctan(x) represents the inverse tangent function. In this equation, x is the input (or independent variable) and y is the output (or dependent variable).
The arctan(x) function, also known as the inverse tangent function or atan(x), is the inverse of the tangent function. It is denoted as “arctan” or “tan^(-1)”, and it returns the angle whose tangent is x. In other words, if we have a right triangle with an angle θ, where the opposite side is x and the adjacent side is 1, then arctan(x) will give us the value of θ.
The arctan function maps the real numbers from negative infinity to positive infinity to the interval (-π/2, π/2). It also has a periodicity of π, meaning that arctan(x + π) = arctan(x) for any value of x.
Graphically, the arctan function is symmetric about the origin. It starts at -π/2 for x approaching negative infinity, increases towards 0 as x increases, and approaches π/2 for x approaching positive infinity.
If you want to find the value of arctan(x) for a specific value of x, you can use either a calculator or consult an arctan table. Keep in mind that the output of the arctan function is always in radians.
For example, if we have x = 1, then y = arctan(1) = π/4 radians (or approximately 0.7854).
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