Exercise 7 (a).  Find   [Graphics:Images/MapTrigonometricFunModHome_gr_450.gif].  

Solution 7 (a).

Answer.   [Graphics:../Images/MapTrigonometricFunModHome_gr_451.gif].  

Solution.  Recall that   [Graphics:../Images/MapTrigonometricFunModHome_gr_452.gif]   so that

                    [Graphics:../Images/MapTrigonometricFunModHome_gr_453.gif].

Then

                    [Graphics:../Images/MapTrigonometricFunModHome_gr_454.gif]  

We are done.   

Aside.  We can look at a graph.

                    [Graphics:../Images/MapTrigonometricFunModHome_gr_455.gif]

                    The curve   [Graphics:../Images/MapTrigonometricFunModHome_gr_456.gif]   is asymptotic to the line   [Graphics:../Images/MapTrigonometricFunModHome_gr_457.gif].  

                    Hence,   [Graphics:../Images/MapTrigonometricFunModHome_gr_458.gif].

We are really done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/MapTrigonometricFunModHome_gr_459.gif]

[Graphics:../Images/MapTrigonometricFunModHome_gr_460.gif]


[Graphics:../Images/MapTrigonometricFunModHome_gr_461.gif]

[Graphics:../Images/MapTrigonometricFunModHome_gr_462.gif]


[Graphics:../Images/MapTrigonometricFunModHome_gr_463.gif]

[Graphics:../Images/MapTrigonometricFunModHome_gr_464.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



This solution is complements of the authors.

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2008 John H. Mathews, Russell W. Howell