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Introduction
Introduction of 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.

Principal Value

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.

Inverse Trigonometric Functions (Principal Value Branches) table with their Domain and Range

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

Graph of sin x and sin-1 x

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. sin x sin x inverse

Graph of cos x and cos-1 x

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. cos x cos x inverse

Graph of tan x and tan-1 x

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. tan x tan x inverse

Graph of cot x and cot-1 x

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. cot x cot x inverse

Graph of sec x and sec-1 x

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. sec x sec x inverse

Graph of cosec x and cosec-1 x

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. cosec x cosec x inverse

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