I have a test coming up today and I was going over our past midterms and this question came up. I tried it but its not working, please any hints or solution in how to do it will be really helpful.
Question:
Consider the polar curve $r = min(1 - cos(\theta), 1 + sin(\theta))$ and $\theta \in [0, \frac{3\pi}{2}]$
a) Sketch the curve. TO sketch the curve you will need to rewrite r as a case define function $r = 1 - cos(\theta), \theta \in [a, b]$ and $1 + sin(\theta), \theta \in [c, d]$
with $a, b, c, d$ to be determined.
b) Find the length of the curve. In the final answer you don't need to evaluate the values of sin or cos.
My attempt:
So what I did was I graphed the polar curve of $1 - cos(\theta)$ and $1 + sin(\theta)$ I drew it on the same graph.
I can see that there is a point of intersection and that a and d maybe be 0. But I am not understanding the question properly. My friend told me that I need to use $tan(\theta) = -1$ but I am really confused.
and b is followed by a, please any hints or solutions would be really appreciated.
Thank you