You should read the section before attempting any reading questions or problems. Remember that you are responsible for all definitions and examples. Also remember to keep the answers to the reading questions on a separate piece of paper; these will be randomly collected from time to time.
1) Consider example 1.4.2.
a) Why does q = p/3 imply r =-4?
b) List three other possibilities for (r, q, w) which differ from the triples given in your text:
(4, 4p/3, 3) and (-4, p/3, 3).
2) Note example 1.4.3 illustrates why the system (r, q, w) is called cylindrical coordinates and example 1.4.8. similarly shows why the system (r, q, F) is called spherical coordinates. Graph the equation r = 4 in spherical coordinates.
3) Both of equations (1.4.5) and (1.4.12) for converting from rectangular coordinates require x to be nonzero. How would you determine q if x=0?
4) Give an example of an equation which is easier to analyze (graph) in cylindrical coordinates.
5) Give an example of
an equation which is easier to analyze (graph) in spherical coordinates.
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