Question

Use polar coordinates to describe the plane region in the first quadrant and between the circles centered at the origin with radii 3 and 5, respectively?

a) 3≤r≤5,0≤θ≤π/2
b) 0≤r≤5,0≤θ≤π/6
c) 3≤r≤5,0≤θ≤π/6
d) 0≤r≤5,0≤θ≤π/2

Answer 1

To describe a plane region in the first quadrant and between two circles centered at the origin with radii 3 and 5, we use polar coordinates. The correct description is (a) 3≤r≤5, 0≤θ≤π/2.

Step-by-step explanation:

In this problem, we are asked to describe a plane region using polar coordinates. The region is in the first quadrant and is between two circles centered at the origin with radii 3 and 5, respectively. To describe this region, we need to find the range for both the radial coordinate (r) and the angular coordinate (θ).

In the first quadrant, the angle θ ranges from 0 to π/2. The radial coordinate r ranges from the circle with radius 3 to the circle with radius 5. So, the correct answer is (a) 3≤r≤5, 0≤θ≤π/2.