Homework 11 – Additional Exercises
Problem 1 concerns the polar description of a plane curve (see section 10.3).
Problems 2 – 5 regard the areas and points of intersection of polar curves (see section 10.4).
1. Show that the polar equation r = a sin θ + b cos θ, where ab s 0,
represents a circle, and find its center and radius.
Find the area of the shaded region in problems 2 and 3.
2. r = 1 + cos θ
3. r = sin 2θ.
4. Sketch the curve: r = 3 cos θ and find the area it encloses.
5. Find all points of intersection of the curves:
r = sin θ and r = sin 2θ.