Question

Classify the limaçon represented by the equation r=(1/2)-(1/2)sin(theta)

A. Cardioid
B. Dimpled
C. Convex
D. Inner loop

Answer 1

we know that

Limacons are in the form
r=a(+-)b*sin (theta)  or r=a(+-)b*cos (theta)

in this problem
r=a(+-)b*sin (theta)
so
is symmetric to y axis
a=1/2
b=1/2
a/b=1---------> Cardioid (hearth shaped)

see the attached figure

the answer is the option
A. Cardioid