Classify the limaçon represented by the equation r = 2 + 2 sin θ.

Question

(1 point)
Responses

cardioid
cardioid

convex
convex

dimpled
dimpled

inner loop

Answer 1

The limaçon represented by the equation \( r = 2 + 2 \sin \theta \) is classified as a cardioid.

This is identified because the general form \( r = a + b \sin \theta \) or \( r = a + b \cos \theta \) behaves like a cardioid when \( a = b \). Here, both are equal to 2. Hence, the correct response is cardioid.