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Learn how to find the domain and range of inverse trigonometric functions using rules and examples. The domain of tan-1(x) is all real numbers and the range is [-π/2, π] or [0, π].
In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [1] cyclometric, [2] or arcus functions [3]) are the inverse functions of the trigonometric functions, under suitably restricted domains.
Sal finds the formula for the inverse function of g(x)=tan(x-3π/2)+6, and then determines the domain of that inverse function.
The principal value of the inverse tangent is implemented as ArcTan [z] in the Wolfram Language. In the GNU C library, it is implemented as atan (double x). The inverse tangent is a multivalued function and hence requires a branch cut in the complex plane, which the Wolfram Language 's convention places at and .
Arctan function is the inverse of the tangent function. It is usually denoted as arctan x or tan -1 x. The basic formula to determine the value of arctan is θ = tan -1 (Perpendicular / Base).
Sal finds the formula for the inverse function of g(x)=tan(x-3π/2)+6, and then determines the domain of that inverse function.
The domain and range of the tan function are the range and domain of its inverse tan function respectively. i.e., arctan x (or) tan-1 x : R → (-π/2, π/2). Therefore, the domain of tan inverse x is R.
