Question: 1) Consider the region enclosed by the curve r = 4cosθ and the rays θ = 6Π and θ = 4Π - a.
a) Sketch the region.
b) Calculate the area of the region analytically.
c) Compute the perimeter of the region.
2) Consider the cardiod r = 1 - cosθ.
a) Analytically determine the total enclosed area of the cardiod.
b) Compute the perimeter of the cardiod .
c) Find the area bounded by the cardiod and the y-axis in the first quadrant.
d) Find the area bounded by the caridiod, the polar axis and the y-axis in the third quadrant.
3) Let A be the region in the interior of r = 4 cos θ and in the exterior of r = 1. Calculate both the area and the perimeter of region A.
4) Find both the area and the perimeter of the region enclosed by r = 0.5 and one petal of the rose curve r = cos 3θ.
5) Compute the area of the region between the inner and outer loop of the limacon r = 2 cos θ - 1.