The region enclosed by the curves and is to be analyzed
MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions
Problem
The region enclosed by the curves r=3sinθ and r=1 is to be analyzed. Which symmetry can most effectively be used to reduce the amount of computation needed to find the area of this region?
(a) Symmetry about the polar axis (x-axis) only
(b) Rotational symmetry about the origin through an angle π
(c) Symmetry about the line θ=2π only
(d) No useful symmetry is present; the integral must be evaluated over 0≤θ≤2π