How to Create a Wavy Circle Function on a Graph?

[Bushy]

If I graph $x+ \sin x $ it looks like a wavey line.

I want a function that looks like a wavey circle. I thought $\sqrt{r^2-x^2}+\sin x$ may work and played around with values for r, no such luck. Does anyone know a function to achieve this?

 

[Jameson]

\(\displaystyle \sqrt{30-x^2}+\frac{(\sin x)^2}{4}\) seems sort of close. I don't know exactly what you're picturing in your head but you can adjust the fluctuations by manipulating sin(x).

 

[Bushy]

Yep that's on the right track, was looking to see more visible oscillations on the cirlce if that makes sense.

This is more of a general interest type question

 

[Ackbach]

Seems like polar coordinates might be useful here. Something like
$$r=1+0.1\sin(10 \theta)$$
might work.

 

[DeusAbscondus]

I'm trying to participate in this thread by adding a little graph, but I can't get the hang of the upload facility:
I have 2 objects visible in the upload box which i wish to delete so as to come under my quota but can't for the life of me see how to delete.

Without a delete, I can't upload the graph I want to share.

Anyone browsing able to help?

DeusAbs

 

[Jameson]

I'm trying to participate in this thread by adding a little graph, but I can't get the hang of the upload facility:
I have 2 objects visible in the upload box which i wish to delete so as to come under my quota but can't for the life of me see how to delete.

Without a delete, I can't upload the graph I want to share.

Anyone browsing able to help?

DeusAbs

Try deleting it http://www.mathhelpboards.com/profile.php?do=editattachments? If that doesn't work then tinyimage will let you upload it there and you can just link to it from here.

 

[Bushy]

I'm trying to participate in this thread by adding a little graph, but I can't get the hang of the upload facility:
I have 2 objects visible in the upload box which i wish to delete so as to come under my quota but can't for the life of me see how to delete.

Without a delete, I can't upload the graph I want to share.

Anyone browsing able to help?

DeusAbs

What is the function?

 

[DeusAbscondus]

Try deleting it http://www.mathhelpboards.com/profile.php?do=editattachments? If that doesn't work then tinyimage will let you upload it there and you can just link to it from here.

Hey guys,
I've taken Jameson wavy semi-circe and plotted inflection points on it (with some labour, got to tell you, as Geogebra found it beyond its brief to do it automatically) using perpendicular lines linking $f(x)$ with zeroed $f''(x)$

I've included it as a png screenshot from my pc, as I have been unsuccessful so far at uploading graphs or pics any other way.

Regs,
Deus Abs

PS this is very much in the category of enthusiastic beginner of calc with time on his hands, in the middle of coming to terms with the meaning of second derivative.

 

[CaptainBlack]

Wavey Circle:

>t=0:0.01:2*pi;
>
>r=1+0.1*cos(10*t);
>
>x=r*cos(t);
>y=r*sin(t);
>
>xplot(x,y);
>

CBView attachment 316

 

[DeusAbscondus]

What is the function?

$f(x)=\sqrt{30-x^2}+\frac{sin(x^2}{4}$