Question

Is there a way to tell if an equation is a cardioid or a limacon without graphing it? I'm supposed to tell what shape r=2+2sin theta is, but cardioid and limacon equations look the same. I know cardioids come from limacons, so maybe I should say that.

Answer 1

@Astrophysics if you aren't busy, can you help me?

Answer 2

@Ashleyisakitty @satellite73 @jim_thompson5910 @TheSmartOne @Nnesha @Loser66 @wio @sammixboo @kropot72

Answer 3

Not quite, you need to know what the equations look like, cardoids are as the following \[r = a \pm a \cos \theta~~~\text{and}~~~r = a \pm a \sin \theta\] see if you can figure out these graphs.

And limacons are in the following form
\[r = b+a \cos \theta~~~\text{and}~~~r = b + a \sin \theta\] horizontal and vertical respectively. And they can be looped, if b<a, dimpled a<b<2a, and in a convex form if 2a less than equal to b.

Notice that if a = b, then it's a cardioid.