Q) Sketch the region given in polar coordinates by $1\leq r\leq 2$, $\frac{\pi}{4} \leq \theta \leq \pi$
Comments:
I find this question particularly difficult because of the format. I've had to plot polar coordinates in the form (r, theta) and sketch curves but I am unsure of how to go about sketching a region set up like this. I am just lost.
I am guessing that if I find the angles for theta first i can color in between the radius creating what looks like a cut out of a dough nut. Is this correct?
Any tips would be wonderful!
Best Answer
$1\le r\le 2$ by itself is a "washer" or annulus with inner radius $1$ and outer radius $2$.
$\pi/4\le\theta\le \pi$ by itself sweeps out a circular wedge which starts at $\theta=\pi/4$ and ends at $\theta=\pi$.
Combining these two: