# Graphing the sum of functions

#### Bushy

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

I want a fucntion 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

Staff member
$$\displaystyle \sqrt{30-x^2}+\frac{(\sin x)^2}{4}$$ 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

##### Member
Yep thats 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

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

#### DeusAbscondus

##### Active member
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

Staff member
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 here? If that doesn't work then tinyimage will let you upload it there and you can just link to it from here.

#### Bushy

##### Member
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

##### Active member
Try deleting it here? 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

##### Well-known member
Wavey Circle:

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

CB