Which graph shape represents the polar curve r = 1 + 4sin(θ)? a cardioid
a rose curve
a limaçon with an inner loop
a limaçon without an inner loop

A cardioid

Step-by-step explanation:

A cardioid is a curve in the shape of a heart traced by a point on the circumference of a circle as it rolls around a fixed circle of the same radius.

The equation of vertical cardioid is ±

Given the polar curve is 4

This is an equation of vertical cardioid.

So, it represents a cardioid.