For a function to have an inverse, it must be one-to-one. Sometimes, when a function is not one-to-one, one can restrict its domain to make it one-to-one.

The inverse trigonometric functions are the inverse functions of the trigonometric functions. Because of their periodic nature, the trigonometric functions are not one-to-one. By restricting their domains, we can construct one-to-one functions from them.

Remembering that the domain of a function and the range of its inverse are the same, we can define the following inverse trigonometric functions :

The inverse trigonometric functions are the inverse functions of the trigonometric functions. Because of their periodic nature, the trigonometric functions are not one-to-one. By restricting their domains, we can construct one-to-one functions from them.

Remembering that the domain of a function and the range of its inverse are the same, we can define the following inverse trigonometric functions :

- The inverse sine function , denoted by sin
^{-1}is the function with domain [-1,1] , range [-π/2,π/2] , defined by y = sin^{-1}x => x = siny .The inverse sine function is also called arcsine , it is denoted by arcsin. - The inverse cosine function , denoted by cos
^{-1}is the function with domain [-1,1] , range [0,π] , defined by y = cos^{-1}x => x = cosy The inverse cosine function is also called arccosine , it is denoted by arccos. - The inverse tangent function , denoted by tan
^{-1}is the function with domain R , range [-π/2,π/2] , defined by y = tan^{-1}x => x = tany The inverse tangent function is also called arctangent , it is denoted by arctan.

Inverse trigonometry is little bit difficult than trigonometry but its necessary to understand the whole Trigono concept.This blog is really helpful in learning that.

ReplyDelete