Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate. r = 3 + 2 cos ⁡ θ r=3+2\cos\theta r = 3 + 2 cos θ

In this problem, we're asked to identify whether the given equation is that of a cardioid, a limosome, a rose, or a lemniscate. And the equation that we're given here is r equals 3 plus 2 times the cosine of theta. Now I can immediately narrow this down to 2 because I know that only a cardioid and limosome will contain addition or subtraction, so it can't be a rose or a lemniscate. Now I want to pay attention to those a and b values here. Now since they're not the same, this cannot be a cardioid leaving me with just one final option, a limason. So this is the equation of a limason r equals 3 +2cosine theta. Thanks for watching and let me know if you have questions.