Thursday, July 19, 2012

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.
This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

1 comment:

  1. 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.

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