Inverse Trigonometric Functions - I

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 sine function , denoted by sin^-1 is the function with domain [-1,1] , range [-π/2,π/2] , defined by y = sin^-1x => 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^-1x => 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^-1x => x = tany The inverse tangent function is also called arctangent , it is denoted by arctan.

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