Give inequalities for r and θ which describe the region below in polar coordinates.

Question

Give inequalities for r and θ which describe the region below in polar coordinates. The two arcs shown are circular, and the region is between the two arcs and between the y-axis and line graphed, which is y=x.

Answer 1

The distance from (0,0) to (3,3) is, by the distance formula, 3√2 and the distance from (0,0) to (5,5) is 5√2.

3 √2 ≤ r ≤ 5√2

π/4 ≤ θ ≤ π/2