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Introduction

Inverse Trigonometry

An inverse trigonometry functions are that functions in which inverse functions are used in trigonometry. Trigonometry functions are sine, cosine, tangent, cotangent, secant, and cosecant.

The value of an inverse trigonometric functions which lies in the range of principal branch is called the principal value of that inverse trigonometric functions.

The following table gives the inverse trigonometric function (principal value branches) along with their domains and ranges.

The graph of the function y = sin^{-1} x can be obtained from the graph of y = sin x by interchanging x and y axes.
The graphs of y = sin x and y = sin^{-1} x are as given in Figures.
The dark portion of the graph of y = sin^{-1} x represent the principal value branch.

The graph of the function y = cos^{-1} x can be obtained from the graph of y = cos x by interchanging x and y axes.
The graphs of y = cos x and y = cos^{-1} x are as given in Figures.
The dark portion of the graph of y = cos^{-1} x represent the principal value branch.

The graph of the function y = tan^{-1} x can be obtained from the graph of y = tan x by interchanging x and y axes.
The graphs of y = tan x and y = tan^{-1} x are as given in Figures.
The dark portion of the graph of y = tan^{-1} x represent the principal value branch.

The graph of the function y = cot^{-1} x can be obtained from the graph of y = cot x by interchanging x and y axes.
The graphs of y = cot x and y = cot^{-1} x are as given in Figures.
The dark portion of the graph of y = cot^{-1} x represent the principal value branch.

The graph of the function y = sec^{-1} x can be obtained from the graph of y = sec x by interchanging x and y axes.
The graphs of y = sec x and y = sec^{-1} x are as given in Figures.
The dark portion of the graph of y = sec^{-1} x represent the principal value branch.

The graph of the function y = cosec^{-1} x can be obtained from the graph of y = cosec x by interchanging x and y axes.
The graphs of y = cosec x and y = cosec^{-1} x are as given in Figures.
The dark portion of the graph of y = cosec^{-1} x represent the principal value branch.

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