Question

What values of theta ( 0< theta< 2pi) do maximum r-values occur on the graph the polar equation r = 3 + 2 sin theta? Note that the maximum r-value occurs at a point that is the maximum distance from the pole.

a. 0, pi/2, pi, 3pi/2
b. 0, pi
c. pi/2
d. pi/2, 3pi/2

Answer 1

C

Explanation:

edge

Answer 2

Correct option: c -> pi/2

Explanation:

To have the maximum value of r, we need to have sin(theta) = 1, so we will have r = 3 + 2*1 = 5

For other values of sin(theta), r will be smaller than 5.

So, to have sin(theta) = 1, there is only one possible angle, that is theta = 90 degrees.

To convert from degree to radians, we can use a rule of three:

180 degrees -> pi radians

90 degrees -> x radians

x * 180 = 90*pi

x = 90*pi/180 = pi/2

Correct option: c