This investigation will be an exciting and rewarding one, as I
have never had any dealings with Polar Equations.
As you begin your journey
through the hall of pictures, first, jot down any notes
that you readily notice and any questions that you may have. Then,
go back to each "picture," pause for a moment (that
moment should be 5 to 15 minutes), and thoroughly examine each figure. What can you say about each? Where does the graph
of each equation lie? How does its position in the Cartesian coordinate
system have a relation to that of the other graphs? How are the
equations of each graph similar? how are they different? How do
you know this? Make a conjecture about your findings (your conjecture
does not have to be the same as your partner's).
At the close of your journey,
create your own graph that can go in the "hall of pictures."
Be sure to include all of the above equations in your pictorial
debut! CLICK HERE to go back to the list of equations.
Give proof to what you say...make sure your partner can "see"
the same things you are seeing. Make sure that you and your partner
can agree on the above questions. If there is any disagreeement,
talk it out...if you two still cannot hash it out find out more
information from other resources (e.g. other classmates). Then
if all else fails, we will all discuss the matter in our class
How was your journey through
the hall of pictures? Hopefully, it was a pleasant and surprising
one! Now CLICK
HERE to go back to
the top to fully begin your examination.