Barrons AP Calculus - David Bock

FIGURE N1–14
A polar function defines a curve with an equation of the form r = f ( ). Some common polar functions
include:

EXAMPLE 17

Consider the polar function r = 2 + 4 sin.

(a) For what values of in the interval [0,2π] does the curve pass through the origin?

(b) For what value of in the interval [0,π/2] does the curve intersect the circle r = 3?

SOLUTION:

(a) At the origin r = 0, so we want 2 + 4 sin = 0. Solving for yields which occurs at

(b) The curves r = 2 + 4 sin and r = 3 intersect when 2 + 4 sin = 3, or From the

calculator we find = arcsin

FIGURE N1–15