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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    Explanation:
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  • Q5

    Write the domain and range of the function given below:
    f(x) = sin-1x.

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