For various a and b, investigate
LetÕs set a and b equal to a range of values and see what happens and what relationships can be seenÉ
LetÕs begin with situations where a = b and they equal one:
This equation results in a circle with center at the origin and a radius of one.
Now, letÕs change a and b to 2:
ItÕs the same circle. How can that be?
LetÕs change a and b to 3:
What happens if we make a and b less than one? How about 0.5?
Aha! We get a half-circle! I think this means that if a and b are more than one then the same points are graphed, thereby just going over the previous points.
What if a and b are different?
a=1 and b=2
This is a much different graph! The limits are still one, but now it looks like a bowÉWhat will happen if a=1 and b=3?
Does b determine the number of sections if a and b arenÕt equal?
It would appear soÉat least when a=1. Now IÕd like to keep b constant and vary aÉ
The limit appears still to be one. I need to look at more graphsÉ
This looks just like the graph where a=1 and b=3, but itÕs been turned and visually appears to be centered on the y-axis as opposed to the other graph, which appeared to be centered on the x-axis. Now a seems to be determining the number of sections.