Why is $r=sin (theta)$ graphing differently than $x^2+y^2=y$?
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I do most of my graphing using Desmos, and also use graphing as a visual check for some of the math that I'm a little more wary of when I don't have access to someone to double check my work. I was doing something when I noticed a discrepancy which boils down to the title question. Above is a picture of Desmos's graph of those two equations. If it's just a problem with the calculator, I'll soon report it as a bug and be very relived that math isn't broken.
graphing-functions
edited Nov 21 at 18:00
idea
1,96231024
asked May 21 at 2:34
Aaron Quitta
323214
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show 2 more comments
up vote
1
down vote
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I do most of my graphing using Desmos, and also use graphing as a visual check for some of the math that I'm a little more wary of when I don't have access to someone to double check my work. I was doing something when I noticed a discrepancy which boils down to the title question. Above is a picture of Desmos's graph of those two equations. If it's just a problem with the calculator, I'll soon report it as a bug and be very relived that math isn't broken.
graphing-functions
edited Nov 21 at 18:00
idea
1,96231024
asked May 21 at 2:34
Aaron Quitta
323214
1
I can't see your graphs, but I'm guessing you didn't tell Desmos (however one does that) that the first one should be in polar coordinates. Is there a place to select "polar" as opposed to "cartesian"?
– Ted Shifrin
May 21 at 2:42
There is no need for that, I'll attach an image instead of the graph, or you can try it yourself just by typing the 2 equations in.
– Aaron Quitta
May 21 at 2:46
1
When I opened the link to your graph, it was behaving a little buggy. After switching between rectangular grid and polar grid and turning graphs on and off, it eventually righted itself. In particular using just 1 and 3 plots correctly for me. Also went to Default Zoom. Bad cache maybe.
– sharding4
May 21 at 2:46
@TedShifrin That isn't the issue. It appears (to me) to be the result of a loss-of-precision or an issue with rounding. Basically, the two curves are very, very close to each other, but off by a small amount (maybe a millionth of a unit?).
– Xander Henderson
May 21 at 2:46
I remove myself from this discussion.
– Ted Shifrin
May 21 at 2:48
|
show 2 more comments
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I do most of my graphing using Desmos, and also use graphing as a visual check for some of the math that I'm a little more wary of when I don't have access to someone to double check my work. I was doing something when I noticed a discrepancy which boils down to the title question. Above is a picture of Desmos's graph of those two equations. If it's just a problem with the calculator, I'll soon report it as a bug and be very relived that math isn't broken.
graphing-functions
edited Nov 21 at 18:00
idea
1,96231024
asked May 21 at 2:34
Aaron Quitta
323214
I do most of my graphing using Desmos, and also use graphing as a visual check for some of the math that I'm a little more wary of when I don't have access to someone to double check my work. I was doing something when I noticed a discrepancy which boils down to the title question. Above is a picture of Desmos's graph of those two equations. If it's just a problem with the calculator, I'll soon report it as a bug and be very relived that math isn't broken.
graphing-functions
graphing-functions
edited Nov 21 at 18:00
idea
1,96231024
asked May 21 at 2:34
Aaron Quitta
323214
edited Nov 21 at 18:00
idea
1,96231024
asked May 21 at 2:34
Aaron Quitta
323214
edited Nov 21 at 18:00
idea
1,96231024
edited Nov 21 at 18:00
idea
1,96231024
edited Nov 21 at 18:00
idea
1,96231024
1,96231024
asked May 21 at 2:34
Aaron Quitta
323214
asked May 21 at 2:34
Aaron Quitta
323214
asked May 21 at 2:34
Aaron Quitta
323214
323214
1
I can't see your graphs, but I'm guessing you didn't tell Desmos (however one does that) that the first one should be in polar coordinates. Is there a place to select "polar" as opposed to "cartesian"?
– Ted Shifrin
May 21 at 2:42
There is no need for that, I'll attach an image instead of the graph, or you can try it yourself just by typing the 2 equations in.
– Aaron Quitta
May 21 at 2:46
1
When I opened the link to your graph, it was behaving a little buggy. After switching between rectangular grid and polar grid and turning graphs on and off, it eventually righted itself. In particular using just 1 and 3 plots correctly for me. Also went to Default Zoom. Bad cache maybe.
– sharding4
May 21 at 2:46
@TedShifrin That isn't the issue. It appears (to me) to be the result of a loss-of-precision or an issue with rounding. Basically, the two curves are very, very close to each other, but off by a small amount (maybe a millionth of a unit?).
– Xander Henderson
May 21 at 2:46
I remove myself from this discussion.
– Ted Shifrin
May 21 at 2:48
|
show 2 more comments
1
I can't see your graphs, but I'm guessing you didn't tell Desmos (however one does that) that the first one should be in polar coordinates. Is there a place to select "polar" as opposed to "cartesian"?
– Ted Shifrin
May 21 at 2:42
There is no need for that, I'll attach an image instead of the graph, or you can try it yourself just by typing the 2 equations in.
– Aaron Quitta
May 21 at 2:46
1
When I opened the link to your graph, it was behaving a little buggy. After switching between rectangular grid and polar grid and turning graphs on and off, it eventually righted itself. In particular using just 1 and 3 plots correctly for me. Also went to Default Zoom. Bad cache maybe.
– sharding4
May 21 at 2:46
@TedShifrin That isn't the issue. It appears (to me) to be the result of a loss-of-precision or an issue with rounding. Basically, the two curves are very, very close to each other, but off by a small amount (maybe a millionth of a unit?).
– Xander Henderson
May 21 at 2:46
I remove myself from this discussion.
– Ted Shifrin
May 21 at 2:48
1
1
I can't see your graphs, but I'm guessing you didn't tell Desmos (however one does that) that the first one should be in polar coordinates. Is there a place to select "polar" as opposed to "cartesian"?
– Ted Shifrin
May 21 at 2:42
I can't see your graphs, but I'm guessing you didn't tell Desmos (however one does that) that the first one should be in polar coordinates. Is there a place to select "polar" as opposed to "cartesian"?
– Ted Shifrin
May 21 at 2:42
There is no need for that, I'll attach an image instead of the graph, or you can try it yourself just by typing the 2 equations in.
– Aaron Quitta
May 21 at 2:46
There is no need for that, I'll attach an image instead of the graph, or you can try it yourself just by typing the 2 equations in.
– Aaron Quitta
May 21 at 2:46
1
1
When I opened the link to your graph, it was behaving a little buggy. After switching between rectangular grid and polar grid and turning graphs on and off, it eventually righted itself. In particular using just 1 and 3 plots correctly for me. Also went to Default Zoom. Bad cache maybe.
– sharding4
May 21 at 2:46
When I opened the link to your graph, it was behaving a little buggy. After switching between rectangular grid and polar grid and turning graphs on and off, it eventually righted itself. In particular using just 1 and 3 plots correctly for me. Also went to Default Zoom. Bad cache maybe.
– sharding4
May 21 at 2:46
@TedShifrin That isn't the issue. It appears (to me) to be the result of a loss-of-precision or an issue with rounding. Basically, the two curves are very, very close to each other, but off by a small amount (maybe a millionth of a unit?).
– Xander Henderson
May 21 at 2:46
@TedShifrin That isn't the issue. It appears (to me) to be the result of a loss-of-precision or an issue with rounding. Basically, the two curves are very, very close to each other, but off by a small amount (maybe a millionth of a unit?).
– Xander Henderson
May 21 at 2:46
I remove myself from this discussion.
– Ted Shifrin
May 21 at 2:48
I remove myself from this discussion.
– Ted Shifrin
May 21 at 2:48
|
show 2 more comments
1 Answer
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The commenters guessing it was a precision error were correct. As far as I can tell, it's an unfortunate consequence of the way Desmos graphs polar equations. Desmos graphs nearly all Cartesian equations with smooth curves, but it uses minuscule line segments to approximate the graphs of polar equations.
For a rough comparison, you can graph $r=sin(9theta)$ and $y=0.77sin(9x+2)$ (in green and purple below, respectively), which have somewhat similar curvature at their relative extrema, and zoom in on the approximate intersection of two extrema in the first quadrant, at about $(0.64,0.765)$ to see how differently Desmos plots both curves (notice also that when zoomed out, they both look smooth). I suspect you were seeing a similar kind of effect when you zoomed in very far on your graph.
answered Nov 21 at 17:21
Robert Howard
1,9181822
add a comment |
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up vote
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The commenters guessing it was a precision error were correct. As far as I can tell, it's an unfortunate consequence of the way Desmos graphs polar equations. Desmos graphs nearly all Cartesian equations with smooth curves, but it uses minuscule line segments to approximate the graphs of polar equations.
For a rough comparison, you can graph $r=sin(9theta)$ and $y=0.77sin(9x+2)$ (in green and purple below, respectively), which have somewhat similar curvature at their relative extrema, and zoom in on the approximate intersection of two extrema in the first quadrant, at about $(0.64,0.765)$ to see how differently Desmos plots both curves (notice also that when zoomed out, they both look smooth). I suspect you were seeing a similar kind of effect when you zoomed in very far on your graph.
answered Nov 21 at 17:21
Robert Howard
1,9181822
add a comment |
up vote
0
down vote
The commenters guessing it was a precision error were correct. As far as I can tell, it's an unfortunate consequence of the way Desmos graphs polar equations. Desmos graphs nearly all Cartesian equations with smooth curves, but it uses minuscule line segments to approximate the graphs of polar equations.
For a rough comparison, you can graph $r=sin(9theta)$ and $y=0.77sin(9x+2)$ (in green and purple below, respectively), which have somewhat similar curvature at their relative extrema, and zoom in on the approximate intersection of two extrema in the first quadrant, at about $(0.64,0.765)$ to see how differently Desmos plots both curves (notice also that when zoomed out, they both look smooth). I suspect you were seeing a similar kind of effect when you zoomed in very far on your graph.
answered Nov 21 at 17:21
Robert Howard
1,9181822
add a comment |
up vote
0
down vote
up vote
0
down vote
The commenters guessing it was a precision error were correct. As far as I can tell, it's an unfortunate consequence of the way Desmos graphs polar equations. Desmos graphs nearly all Cartesian equations with smooth curves, but it uses minuscule line segments to approximate the graphs of polar equations.
For a rough comparison, you can graph $r=sin(9theta)$ and $y=0.77sin(9x+2)$ (in green and purple below, respectively), which have somewhat similar curvature at their relative extrema, and zoom in on the approximate intersection of two extrema in the first quadrant, at about $(0.64,0.765)$ to see how differently Desmos plots both curves (notice also that when zoomed out, they both look smooth). I suspect you were seeing a similar kind of effect when you zoomed in very far on your graph.
answered Nov 21 at 17:21
Robert Howard
1,9181822
The commenters guessing it was a precision error were correct. As far as I can tell, it's an unfortunate consequence of the way Desmos graphs polar equations. Desmos graphs nearly all Cartesian equations with smooth curves, but it uses minuscule line segments to approximate the graphs of polar equations.
For a rough comparison, you can graph $r=sin(9theta)$ and $y=0.77sin(9x+2)$ (in green and purple below, respectively), which have somewhat similar curvature at their relative extrema, and zoom in on the approximate intersection of two extrema in the first quadrant, at about $(0.64,0.765)$ to see how differently Desmos plots both curves (notice also that when zoomed out, they both look smooth). I suspect you were seeing a similar kind of effect when you zoomed in very far on your graph.
answered Nov 21 at 17:21
Robert Howard
1,9181822
edited Nov 22 at 3:11
answered Nov 21 at 17:21
Robert Howard
1,9181822
answered Nov 21 at 17:21
Robert Howard
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answered Nov 21 at 17:21
Robert Howard
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1
I can't see your graphs, but I'm guessing you didn't tell Desmos (however one does that) that the first one should be in polar coordinates. Is there a place to select "polar" as opposed to "cartesian"?
– Ted Shifrin
May 21 at 2:42
There is no need for that, I'll attach an image instead of the graph, or you can try it yourself just by typing the 2 equations in.
– Aaron Quitta
May 21 at 2:46
1
When I opened the link to your graph, it was behaving a little buggy. After switching between rectangular grid and polar grid and turning graphs on and off, it eventually righted itself. In particular using just 1 and 3 plots correctly for me. Also went to Default Zoom. Bad cache maybe.
– sharding4
May 21 at 2:46
@TedShifrin That isn't the issue. It appears (to me) to be the result of a loss-of-precision or an issue with rounding. Basically, the two curves are very, very close to each other, but off by a small amount (maybe a millionth of a unit?).
– Xander Henderson
May 21 at 2:46
I remove myself from this discussion.
– Ted Shifrin
May 21 at 2:48