Exercise 5.  Find a parametrization of the curve that is a portion of the circle    that joins the point    to    if  

5 (a).  the curve is the right semicircle.  

Solution 5 (a).

See text and/or instructor's solution manual.

    The first thing that comes to mind is to use the well known parameterization

           for   .  

We are done.   

Aside.  We can let Mathematica double check our work.

        The curve      for    ,   where   

        the initial point is    and the terminal point is  .    

We are done.   

    A second parameterization would be to substitute     in the above parameterization and get

            for    ,
        
which can be written as

            for    .  

        The curve     for   ,   where   

        the initial point is    and the terminal point is  .    

We are done.   

    A third parameterization can be obtained by adjusting the above parameterization to get

            for    .  

        The curve      for   ,    where   

        the initial point is    and the terminal point is  .    

This solution is complements of the authors.

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