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

Exercise 5.    at the points  .  

Solution 5.

See text and/or instructor's solution manual.

Answers.   Here we have    and  ,  and  

                    ,  

                    ,  

                    .  

Solutions.   Here we have    and  .  

5 (a).   At the point  .    

                      

5 (b).   At the point  .    

                      

5 (c).   At the point  .    

                      

We are done.   

Aside.  We can let Mathematica double check our work.

5 (a).   At the point  .    

5 (b).   At the point  .    

5 (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   .  

We are really really done.

Caveat.  At a point    where     we will have

                    .

Applying Theorem 10.2 we see that the mapping   magnifies angles at the vertex by the factor  .

                      For     at    we have      and   ,  and
                      the mapping   magnifies angles at the vertex    by the factor  .

Remark.  In Section 10.4 we will study some trigonometric mappings, including  .

This solution is complements of the authors.

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