MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions
Problem
Let C be the curve described by r=6cosθ. Region R is the entire region enclosed by C.
(a) Convert the equation of C to rectangular form and simplify.
(b) From the equation in part (a), determine the exact center and radius of the curve. State your reasoning.
(c) Find the exact area of R using the geometric information obtained in part (b).
(d) Independently compute the area of R by evaluating an appropriate integral in polar coordinates. Show all steps, and verify that your result agrees with the answer from part (c).