Answer:
Limacon of Pascal
Step-by-step explanation:
The given polar functin is
r =1-2sint
We find that when r =0
2sint =1
sint =1/2
Or t = 60, 120
SO it passes through origin for 60, 120 degrees
There is a loop formed between 30 and 150 and again it completes a big round around the loop
When R=1, we find t =0, pi, 2pi
When R=2, we get sint =-1/2
Hence angles are 210 and 330 degrees
Since sin t lies between -1 and 1 only we have
[tex]-1\leq \frac{1-r}{2} \leq1 \\-2\leq 1-r\leq 2\\[/tex]
When sint =-1, r has maximum 3
and when sint =1, r cannot have -1 but 0
So r can take values between 0 and 3
