Exercise 1.  Find all values of the following.  

1 (e).   .  

Solution 1 (e).

Answer.       where  n  is an integer.

Solution.   Use the Identity in (5-45)      and get:  

                      

Therefore,       where  n  is an integer.

                    The points  .  

We are done.   

Aside.  We can let Mathematica double check our work.

This can be accomplished by performing the computation    .  

We are really done.   

Aside.  The principal value of    can be calculated with Mathematica.

Also, we can substitute  n = 1  into the general formula    and get

We are really really done.

                    The point    and the principal value image point  .  

Remark.  We will study mappings with the trigonometric functions in Section 10.4 and in some of the applications that follow in Chapter 11.

This solution is complements of the authors.

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