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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If graph of f(x) = tan(-x) is, then the graph of f-1(x) isMarks:1
If the graph of f(x) is given below, then the graph of f-1(x) is
Write the domain and range of the function given below:
f(x) = sin-1x.Marks:1