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 oneone and onto function.
• In other words, a function ‘f’ is called invertible if and only if the function ‘f ’ is oneone and onto.
• To check whether a function is a oneone function or not, the horizontal line test is used. A horizontal line intersects a oneone function at only one point. However, if it intersects the graph at more than one point, then the function is not oneone.
• 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, OneOne functions, Onto functions, Principle values of Inverse of trigonometric functions
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Q2
The domain of the function f(x) = sin^{1}x + cos^{1}x + cosec^{1}x + cot^{1}x + tan^{1}x 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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Q5
Write the domain and range of the function given below:
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