Math 104
Activity
Polar Graph Exploration
Name:
1. Use a graphing calculator or Maple to graph the polar function r  cos( 2 ) , and
sketch the result here. Tell the values of  that must be cycled through (that is the
domain) to make the graph be a closed curve.
2. Now graph r  cos(3 ) , r  cos( 4 ) , r  cos(5 ), giving rough sketches of them
here.
3. These graphs are all called rose curves, and each little piece is called a petal. Give a
two-part rule that tells the number of petals for the polar function.
r  cos( n ), where n is an integer , and the values that  has to cycle through in
order to print out the whole graph.
Bonus (only if time): Now try non-integer multiples of  . Graph
a
a
r  cos(  ), where a, b are integers and a  b and is in lowest ter ms and repeat the
b
b
5
instructions for number 3. Start with r  cos(  ) and give a sketch of it.
2