Problem 62E

Sets in polar coordinates Sketch the following sets of points.

{(r, θ): 1<r<2 and π/6 ≤ θ ≤ π/3}

Solution 62E

Step 1:

We have to sketch {(r, θ): 1<r<2 and π/6 ≤ θ ≤ π/3}

We know that and

Here is the angle and r is the radius

Therefore 1<r<2 is the region between the circles of radius 1 and 2.

And π/6 ≤ θ ≤ π/3 is the region between the angle and

Therefore we get the graph as

The shaded region is {(r, θ): 1<r<2 and π/6 ≤ θ ≤ π/3}