/sci/ - Science & Math » Thread #12197504

55KiB, 640x512, bs3.jpg

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Anonymous Mon 05 Oct 23:07:41 2020 No.12197504 View Reply Original Report

Quoted By: >>12197519 >>12197598 >>12197606 >>12198377

Is it possible to have a straight line in polar coordinates? Like sure theta=c but that is just a boring case. Can you make any arbitrary straight line like in Cartesian coordinates?

Anonymous

Anonymous Mon 05 Oct 2020 23:11:13 No.12197519 Report

Quoted By: >>12197525

>>12197504
of course. represent equation of line in rectangular, then apply coordinate transformation. i'll fill out the details in another post

Anonymous

Anonymous Mon 05 Oct 2020 23:12:13 No.12197525 Report

Quoted By: >>12197635

>>12197519
But will the line still be straight in the polar coordinates?

Anonymous

Anonymous Mon 05 Oct 2020 23:15:42 No.12197531 Report

Quoted By: >>12197541

Something like r = secant(theta)?

Anonymous

View Same Google iqdb SauceNAO wwwas.png, 3KiB, 959x487

Anonymous Mon 05 Oct 2020 23:18:51 No.12197541 Report

Quoted By: >>12197630

>>12197531
A line like this perhaps

Anonymous

Anonymous Mon 05 Oct 2020 23:22:58 No.12197551 Report

Quoted By: >>12197593

>Can you make any arbitrary straight line in polar coordinates?
Yes.

Anonymous

Anonymous Mon 05 Oct 2020 23:33:13 No.12197593 Report

Quoted By: >>12197630

>>12197551
How? What would the equation be?

Anonymous

Anonymous Mon 05 Oct 2020 23:34:28 No.12197598 Report

Quoted By: >>12197609

>>12197504
those are all straight lines

Anonymous

Anonymous Mon 05 Oct 2020 23:36:41 No.12197606 Report

Quoted By: >>12197613

>>12197504
y = rsin(theta)
x = rcos(theta)
y = mx + b
Solve for r.

Anonymous

Anonymous Mon 05 Oct 2020 23:37:46 No.12197609 Report

Quoted By:

>>12197598
Pic not related. Im asking if there is a form of a polar equation for a straight line.

Anonymous

Anonymous Mon 05 Oct 2020 23:39:34 No.12197613 Report

Quoted By: >>12197627

>>12197606
y/sin(theta)
x/cos(theta)

so
y/sin(theta)=x/cos(theta)+b ?

Anonymous

Anonymous Mon 05 Oct 2020 23:46:43 No.12197627 Report

Quoted By:

>>12197613
No, more like plug y and x into the third equation then solve for r. That will give you r in terms of theta only.

Anonymous

View Same Google iqdb SauceNAO polar coords line.jpg, 53KiB, 1303x425

Anonymous Mon 05 Oct 2020 23:46:51 No.12197630 Report

Quoted By: >>12197837

>>12197593
>>12197541

Anonymous

Anonymous Mon 05 Oct 2020 23:48:09 No.12197635 Report

Quoted By:

>>12197525
representations are irrespective of coordinate system

Anonymous

Anonymous Tue 06 Oct 2020 00:42:26 No.12197837 Report

Quoted By: >>12197844

>>12197630
How did you get that equation though anon?

Anonymous

Anonymous Tue 06 Oct 2020 00:45:31 No.12197844 Report

Quoted By: >>12198196

>>12197837
r = sec(fi) is the basic equation for a straight line in polar coordinates. You can then manipulate the line by additional operations.

Anonymous

Anonymous Tue 06 Oct 2020 02:50:02 No.12198196 Report

Quoted By: >>12198201

>>12197844
Yeah polar coordinates are really handy to try to derive equations that have some circularity, and are much faster to compute than the cartesian form. Polar coordinates are underrated. I wish I was polar bear.

Anonymous

Anonymous Tue 06 Oct 2020 02:51:04 No.12198201 Report

Quoted By:

>>12198196
https://www.youtube.com/watch?v=7M67JwFsM_M

Anonymous

View Same Google iqdb SauceNAO gfgdgdsfgdfg.png, 4KiB, 237x86

Anonymous Tue 06 Oct 2020 03:51:52 No.12198358 Report

Quoted By:

Can you get to the line form from this?

Anonymous

Anonymous Tue 06 Oct 2020 04:00:22 No.12198377 Report

Quoted By: >>12198380

>>12197504
r=C is a straight line (cylindrical)
so is theta=C

Anonymous

Anonymous Tue 06 Oct 2020 04:02:07 No.12198380 Report

Quoted By:

>>12198377
actually i guess r=C is a circle but theta=C is a straight line

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