[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 4 KB, 488x451, green_circle.gif [View same] [iqdb] [saucenao] [google]
7244787 No.7244787 [Reply] [Original]

I can't get an intuitive understanding of the parameterization of a circle.

Is there some kind of trick to it?

>> No.7244805

think about polar coordinates (r, theta) where r is the radius of your circle.

let theta range from 0 to 2\pi. it tells you how far around the circle you are

>> No.7244830

>>7244805
Right but the part I'm having trouble with is the formulas.

x = rcost
y = rsint

Sometimes you have to swap sine and cosine, sometimes you have to make one or both negative. How are you supposed to know when to do these things?

>> No.7244833

>>7244830
Depends on what direction the circle is traced.

If it is a normal unit circle you get (cost, sint). For the reverse direction you get (sint, cost)

>> No.7244841

>>7244833
I don't think it's as simple as just having to swap them to reverse the direction. It depends on the starting point as well.

>> No.7244853

>>7244787
My advice?
Kentucky windage and Alabama elevation.

>> No.7244856

>>7244830
> not knowing sohcahtoa
Don't you americans learn anything at school at all ?

>> No.7244857

>>7244841
Would the starting point not be determined by how you allowed t to vary?

Like if you wanted to start on the +y axis you could do t= [pi/2,5pi/2]?

I guess that would work at least. I'm an EE major in Calc 3 right now, and that's how I'd do it on an exam or something.

>> No.7244860

sin is vertical
cos is horizontal
just remember those and the circle falls into place

>> No.7244901

>>7244830
Normally the unit circle is drawn starting from the point (1,0). x must be related to Cos(t) and y must be related to Sin(t) since t = 0.

>> No.7244903

>>7244860
Now I feel bad. I knew those things and the circle didn't fall into place. Maybe I'm just low IQ?

>> No.7244913
File: 253 KB, 700x700, 8b6cb44fa23a73efb9e04da7dd46cf05.gif [View same] [iqdb] [saucenao] [google]
7244913

maybe this will help

>> No.7244916

>>7244903
Sine and Cosine exist as functions solely to describe the y,x coordinates of a circle. (That's how i think of it). You can literally think of the circle as the arbitrary shape drawn when you trace those functions. You can even think of those functions as their taylors, so its even more general and arbitrary.

>> No.7244918

>>7244913
It would help more if it showed every iteration of sine and cosine from every starting point, because apparently the parametric formulas are different depending on the starting point and the direction you want to go.

>> No.7244924

>>7244918
http://www.mathopenref.com/coordparamcircle.html

fuck you

>> No.7244926

>>7244918
Don't try to think of the formulas as changing, think of them as having a phase angle. You can do the math to show that cos(0) = sin (0 + pi/2), k? When you "start" at the point 0,1, and you try to describe the x,y coordinates as (-sin(t), ,cos(t), think of instead as the deafulat cos, sin but with a phase angle of pi/2

>> No.7244998

>>7244924
>>7244926
I appreciate the help but I still don't get it. Sometimes the correct parameterization is x=rsint instead of rcost, depending on the starting point. Every single resource I've looked at online has failed to explain why this is the case or to even mention that this is sometimes the case. Thanks for the help but I believe I am beyond helping at this point.

>> No.7245691

>>7244998
Once again

It depends on the direction that the circle is traced, and your starting point is determined by the range you allow t to vary.

>> No.7245755

>>7244833
the reverse direction would be (cost,-sint)

what you have there is (cos(pi/2-t),sin(pi/2-t))

which does go in the reverse direction, but starts on the y axis

>> No.7245768

>>7244998
Your question is the same as asking why sometimes a circle is x^2 + y^2 = r^2 and other times it's (x-x0)^2 + (y-y0)^2 = r^2.

The answer is, it depends on what your circle is, and what you are trying to do with it.

Maybe if you post some examples were you got confused, then we can see what is making you confused.

>> No.7245831

I never understoof the temporal parametrization myself, so I second OP.

here is the cycloid for you , OP
http://jwilson.coe.uga.edu/EMAT6680Fa07/Gilbert/Assignment%2010/Gayle&Greg-10.htm


does every curve has a paremetrization ?