Question

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

Answer 1

C - a limaçon with an inner loop

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

Answer 2

A cardioid

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.