Module 4  Parametric Equations, Trigonometric and Inverse Trigonometric Functions  
Introduction  Lesson 1  Lesson 2  Lesson 3  Lesson 4  SelfTest  
Lesson 4.4: Inverse Trigonometric Functions  
In Lesson 4.1 you graphed a function and its inverse relation parametrically. In this lesson you will use the same method to graph the inverse relation of a sine function. By restricting the values of Tmin and Tmax you will define the inverse relation so it is a function, also. Inverse Sine Explore the inverse of the sine function by simultaneously graphing the sine function and its inverse using parametric equations.
Notice that as the sine function waves about the xaxis, its inverse waves about the yaxis. Because there is more than one yvalue associated with some xvalues, the inverse relation is not a function. Restricting the Domain of Sine The inverse of the sine function is not a function. But if you restrict the domain of the sine function so that each yvalue in [1, 1] occurs only once, then the inverse of this restricted function will also be a function.
The inverse of this restricted function is a function, however the viewing window is not a good one.
Display only the inverse function by unselecting X_{1T} and Y_{1T} , as described below.
Restricting the domain of y = sin(x) also restricted the range of the inverse relation, which forced each input of the inverse to have exactly one output. The resulting inverse is the function y = sin^{1}x , which is also written as y = arcsin x.


< Back  Next >  
©Copyright
2007 All rights reserved. 
Trademarks

Privacy Policy

Link Policy
