# Basic Concepts of Inverse Trigonometric Functions

## •    Inverse trigonometric functions are the inverse functions of trigonometric functions. While defining the inverse of a trigonometric function, its domain is restricted so that the function becomes both one-one and onto function.  •    In other words, a function ‘f’ is called invertible if and only if the function ‘f ’ is one-one and onto.•    To check whether a function is a one-one function or not, the horizontal line test is used. A horizontal line intersects a one-one function at only one point. However, if it intersects the graph at more than one point, then the function is not one-one.•    The graph of a trigonometric function and the graph of its inverse are symmetrical about the line y = x. The domain of a trigonometric function is the range for its inverse function.•    Representation of inverse of a trigonometric function is as follows: Inverse of sin x is sin–1x. Inverse of cos x is cos–1x. Inverse of tan x is tan–1x. Inverse of cot x is cot–1x. Inverse of sec x is cot–1x. Inverse of cosec x is cosec–1x. •    The value of inverse trigonometric functions, which lies in the range of principal branch, is called the principal value of that inverse trigonometric function.•    Inverse trigonometric functions and its domains and ranges are listed in the following table.Keywords: Inverse of trigonometric functions, Domain and range of Inverse  trigonometric functions, Graphs of inverse trigonometric functions, Invertible functions, One-One functions, Onto functions, Principle values of Inverse of trigonometric functions

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• Q1

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• Q2

The domain of the function f(x) = sin-1x + cos-1x + cosec-1x + cot-1x + tan-1x is

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{-1, 1}.

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• Q3

If graph of f(x) = tan(-x) is, then the graph of f-1(x) is

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.

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• Q4

If the graph of f(x) is given below, then the graph of f-1(x) is

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