# Let D be the region between the circles of radius 6 and radius 8 centered at the

Let D be the region between the circles of radius 6 and radius 8 centered at the origin that lies in the third quadrant.
Express D in polar coordinates.
1) $D=\left\{\left(r,\theta \right)\mid 6\le r\le 8,0\le \theta \le \frac{\pi }{2}\right\}$
2) $D=\left\{\begin{array}{cc}r& \theta \end{array}\right)\mid 6\le r\le 8,\pi \le \theta \le \frac{3\pi }{2}\right\}$
3) $D=\left\{\left(r,\theta \right)\mid 0\le r\le 8,\pi \le \theta \le \frac{3\pi }{2}\right\}$
4) $D=\left\{\left(r,\theta \right)\mid 6\le r\le 8,\pi \le \theta \le 2\pi \right\}$
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dessinemoie
Given:let D be the region between the circles of radius 6 and 8 centered at the origin that lies in the third quadrant express D in polar coordinates.
Here the region D is between the circles with radius r=6,r=8 centered at the origin
that is $6\le r\le 8$ and that lies in quadrant 3
So,
$\pi \le \theta \le \frac{3\pi }{2}$
Therefore,
$D=\left\{\left(r,\therefore \right)\mid 6\le r\le 8,\pi \le \therefore \le 3\pi 2\right\}$
Therefore the 2 nd option is the correct one