Questions: Graph the sets of points whose polar coordinates satisfy the inequalities (0 leq theta leq frac7 pi8, r geq 0).

$Graph the sets of points whose polar coordinates satisfy the inequalities (0 leq theta leq frac7 pi8, r geq 0).$

Transcript text: Graph the sets of points whose polar coordinates satisfy the inequalities $0 \leq \theta \leq \frac{7 \pi}{8}, r \geq 0$.

Solution

Solution Steps

Step 1: Identify the Polar Inequalities

The given polar inequalities are:

$0 \leq \theta \leq \frac{7\pi}{8}$
$r \geq 0$

Step 2: Determine the Region in Polar Coordinates

The inequalities describe a region in polar coordinates where the angle $\theta$ ranges from $0$ to $\frac{7\pi}{8}$ and the radius $r$ is non-negative. This region is a sector of a circle with an angle of $\frac{7\pi}{8}$ radians.

Final Answer

The region is a sector of a circle with an angle of $\frac{7\pi}{8}$ radians and radius $r \geq 0$.

{"axisType": 2, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -3, "ymax": 3}, "commands": ["r = 0"], "latex_expressions": ["$0 \\leq \theta \\leq \\frac{7\\pi}{8}, r \\geq 0$"]}

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