Remember that the polar equation of a limaçon has the following two general forms:
[tex]\begin{gathered} r=a\pm b\sin (\theta) \\ r=a\pm b\cos (\theta) \end{gathered}[/tex]
The only equation that has this general form is:
[tex]r=4+7\sin (\theta)[/tex]
Therefore, this is the only one that represents a limaçon.
