Inverse Cosine Graph

Inverse cosine  is one of the essential  inverse trigonometric function . Its principal values and range is
cos ^-1 : {(y,x)l y = cos x , x `in [ 0, pi]` , y `in` [-1,1]}


In this we deals with determining inverse tangent graphs.

Function	Domain	Principal Value (Range)
y =cos -1 x	R	[ 0, `pi`]

The graph of cos^-1 x is as follows :

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Inverse Cosine Graph : Examples

Example  1 : Draw the inverse cosine graph for the function

                                        y = cos^-1 ( x + 4 ) 

Solution : As it is given   y= cos ^-1 ( x + 4 ) so, there is a horizontal shift in the graph of   y = cos^-1 x by 4 units leftwards 

Graph as shown :

                  

Example  2  : Draw the inverse cosine graph for the function

                                       y = cos^-1 ( x ) - 3 

Solution : As it is given   y = cos^-1 ( x ) - 3

It can also be wirtten as  y + 3  = cos^-1 ( x ) so , there is a vertical shift in the graph of   y =cos ^-1 x by 3 unit downwards

Graph as shown :

                    

Example  3  : Draw the inverse cosine graph for the function

                                        y = cos^-1 ( x + 2 ) and   y = cos^-1 ( x - 1 ) on the same graph 

Solution : As it is given   y = cos^-1 ( x + 2 ) so, there is a horizontal shift in the graph of   y = cos^-1 x by 2 units leftwards and

               for  y = cos ^-1 ( x - 1 ) there is a horizontal shift in the graph of   y = cos^-1 x by 1 unit rightwards

Graph as shown :

             

Inverse Cosine Graph : Practice Problems

Problem 1  :  Draw the inverse cosine graph for the function
                                        y = cos^-1 ( x + 5 )
Problem  2 :  Draw the inverse cosine graph for the function               
                                             y = cos^-1 ( x ) + 6
Problem  3  :  Draw the inverse cosine graph for the function
                                        y = cos^-1 ( x + 1) and   y = cos^-1 ( x - 7 ) on the same graph