Inverse Trigonometric Functions
In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions. While defining the inverse of a trigonometric function, we have to insure that the domain of the trigonometric function is restricted such that the it becomes both one-one and onto function.
Or we can say, ‘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, we use the horizontal line test. 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 the 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.
Using this property, we can find the domain of a trigonometric function, if we know the rage of its inverse.
The value of inverse trigonometric functions, which lies in the range of principal branch, is called the principal value of that inverse trigonometric function.