Instructions For Exercises 2-5.   
Find the angle of rotation    and the scale factor   of the mapping    at the indicated points.  

Exercise 2.     at the points  .  

Solution 2.

See text and/or instructor's solution manual.

Answers.   Here we have    and  ,  and  

                    ,  

                    ,  

                    .  

Solutions.  Here we have    and  .    

2 (a).   At the point  .    

                    

2 (b).   At the point  .    

                        

2 (c).   At the point  .    

                        

We are done.   

Aside.  We can let Mathematica double check our work.

2 (a).   At the point  .    

2 (b).   At the point  .    

2 (c).   At the point  .    

We are really done.   

Aside.  We can let Mathematica illustrate our work.

                      For     at     we have      and   .  

                      For     at     we have      and   .  

                      For     at     we have      and   .  

Remarks.  In Section 2.5 we saw that the reciprocal transformation    maps "generalized circles" onto "generalized circles."

In Section 10.2 we will see that the transformation    will also map "generalized circles" onto "generalized circles."

This solution is complements of the authors.

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