Question

Which graph shape represents the polar curve r = 1 + 4sin(θ)?

Answer 1

Answer:

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 $r=a$ ± $a\sin \theta$

Given the polar curve is $r=$ $1+$ 4 $\sin \theta$

This is an equation of vertical cardioid.

So, it represents a cardioid.

Answer 2

Answer:

C - a limaçon with an inner loop

Step-by-step explanation:

If you have a graphing calculator, use it to plug in the equation.

Based on what you have learned, you will recognize the graph is C