Question

Which of the following polar equations represents a limaçon? r = 7 + sin 4θ r = 4 + 7sin θ r = 4cos θ r = 7cos 4θ

Answer 1

Remember that the polar equation of a limaçon has the following two general forms:

$\begin{gathered} r=a\pm b\sin (\theta) \\ r=a\pm b\cos (\theta) \end{gathered}$

The only equation that has this general form is:

$r=4+7\sin (\theta)$

Therefore, this is the only one that represents a limaçon.