Question

A polar curve is represented by the equation r1 = 3 + 3sin θ.Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.Part B: Is the curve symmetrical to the polar axis or the line theta equals pi over 2 question mark Justify your answer algebraically.Part C: What are the two main differences between the graphs of r1 = 3 + 3sin θ and r2 = 8 + 3cos θ?

Answer 1

Check below, please.

1) Let's plot that curve:

Part A.

Note that this Limaçon is written in the form:

$r=a\pm b\sin(\theta)$

So as we can see, from r=3+3sin(theta) this Limaçon is a Cardiod for there are two positive constants, in this case 3 and 3.

Part C

Let's plot both and analyze it:

Note that while we can see a cardioid for r=3+3sin(theta) we can see that for the other curve a>b so there is a "bump" on the curve.

Apart from the shape itself, we can see that there is symmetry in the

ardiod while we can see any simmetry.