Sketch the curve
Attempt:
when = 0, r = 2
when = , r = -1
when = , r = -2
The graph I got was a circle (not ment to look like an ellipse in the drawing), but the correct answer was a flower
Hello, SyNtHeSiS!
We are expected to recognize this as a "rose curve", a flower-shaped curve.
. . [But it looks more like a daisy.]
There are two basic forms: .
is the length of a "petal".
If is odd, there are petals.
If is even, there are petals.
. . The petals are equally spaced about the center.
We have: .
Since (even), there are 8 petals, spaced 45 degrees apart.
Each petal is 2 units long.
Now where are the petals?
. . When is ?
We have: .
. . . . . . . .
Hence, the "first" petal is on the -line (positive -axis).
You should be able to sketch the graph now.