Mixing
Draw $r ≤ 3 + 2sin (theta)$
$begingroup$
Currently I'm stuck at this fairly easy task. All I have to do is sketch the region $r le 3+2sin theta$. My guess would be that the circle has the origin $(0,3)$ with $r = 2$, as I use the formula $y = b + r sin theta$. But that's completely wrong.
EDIT: I am interesting in the right procedure for drawing a region like this, not the actual plot itself. This was a question for a previous test without the use of calculators.
calculus multivariable-calculus parametric parametrization
asked Jan 23 at 21:27
d salined saline
162
$endgroup$
add a comment |
$begingroup$
Currently I'm stuck at this fairly easy task. All I have to do is sketch the region $r le 3+2sin theta$. My guess would be that the circle has the origin $(0,3)$ with $r = 2$, as I use the formula $y = b + r sin theta$. But that's completely wrong.
EDIT: I am interesting in the right procedure for drawing a region like this, not the actual plot itself. This was a question for a previous test without the use of calculators.
calculus multivariable-calculus parametric parametrization
asked Jan 23 at 21:27
d salined saline
162
$endgroup$
1
$begingroup$
That equation does not define a circle. Why do you say it is a circle?
$endgroup$
– kccu
Jan 23 at 21:32
$begingroup$
That curve is not a circle (or rather, that region is not a disc).
$endgroup$
– Brian Tung
Jan 23 at 21:32
1
$begingroup$
If you're stuck, plot some points for various values of $theta$ and see if you notice anything
$endgroup$
– pwerth
Jan 23 at 21:32
$begingroup$
Oh sorry! I meant region instead of circle. I have plotted with desmos several different sin (θ) and also cos (θ), but I can't see a pattern. Only that sin (θ) is shifted upwards with origin (0,1) and cos (θ) to the right at (1,0).
$endgroup$
– d saline
Jan 23 at 21:42
$begingroup$
Desmos is a good tool to get an idea about the shape of a curve.
$endgroup$
– Math Lover
Jan 23 at 21:48
add a comment |
$begingroup$
Currently I'm stuck at this fairly easy task. All I have to do is sketch the region $r le 3+2sin theta$. My guess would be that the circle has the origin $(0,3)$ with $r = 2$, as I use the formula $y = b + r sin theta$. But that's completely wrong.
EDIT: I am interesting in the right procedure for drawing a region like this, not the actual plot itself. This was a question for a previous test without the use of calculators.
calculus multivariable-calculus parametric parametrization
asked Jan 23 at 21:27
d salined saline
162
$endgroup$
Currently I'm stuck at this fairly easy task. All I have to do is sketch the region $r le 3+2sin theta$. My guess would be that the circle has the origin $(0,3)$ with $r = 2$, as I use the formula $y = b + r sin theta$. But that's completely wrong.
EDIT: I am interesting in the right procedure for drawing a region like this, not the actual plot itself. This was a question for a previous test without the use of calculators.
calculus multivariable-calculus parametric parametrization
calculus multivariable-calculus parametric parametrization
asked Jan 23 at 21:27
d salined saline
162
asked Jan 23 at 21:27
d salined saline
162
edited Jan 24 at 8:43
d saline
asked Jan 23 at 21:27
d salined saline
162
asked Jan 23 at 21:27
d salined saline
162
asked Jan 23 at 21:27
d salined saline
162
162
1
$begingroup$
That equation does not define a circle. Why do you say it is a circle?
$endgroup$
– kccu
Jan 23 at 21:32
$begingroup$
That curve is not a circle (or rather, that region is not a disc).
$endgroup$
– Brian Tung
Jan 23 at 21:32
1
$begingroup$
If you're stuck, plot some points for various values of $theta$ and see if you notice anything
$endgroup$
– pwerth
Jan 23 at 21:32
$begingroup$
Oh sorry! I meant region instead of circle. I have plotted with desmos several different sin (θ) and also cos (θ), but I can't see a pattern. Only that sin (θ) is shifted upwards with origin (0,1) and cos (θ) to the right at (1,0).
$endgroup$
– d saline
Jan 23 at 21:42
$begingroup$
Desmos is a good tool to get an idea about the shape of a curve.
$endgroup$
– Math Lover
Jan 23 at 21:48
add a comment |
1
$begingroup$
That equation does not define a circle. Why do you say it is a circle?
$endgroup$
– kccu
Jan 23 at 21:32
$begingroup$
That curve is not a circle (or rather, that region is not a disc).
$endgroup$
– Brian Tung
Jan 23 at 21:32
1
$begingroup$
If you're stuck, plot some points for various values of $theta$ and see if you notice anything
$endgroup$
– pwerth
Jan 23 at 21:32
$begingroup$
Oh sorry! I meant region instead of circle. I have plotted with desmos several different sin (θ) and also cos (θ), but I can't see a pattern. Only that sin (θ) is shifted upwards with origin (0,1) and cos (θ) to the right at (1,0).
$endgroup$
– d saline
Jan 23 at 21:42
$begingroup$
Desmos is a good tool to get an idea about the shape of a curve.
$endgroup$
– Math Lover
Jan 23 at 21:48
1
1
$begingroup$
That equation does not define a circle. Why do you say it is a circle?
$endgroup$
– kccu
Jan 23 at 21:32
$begingroup$
That equation does not define a circle. Why do you say it is a circle?
$endgroup$
– kccu
Jan 23 at 21:32
$begingroup$
That curve is not a circle (or rather, that region is not a disc).
$endgroup$
– Brian Tung
Jan 23 at 21:32
$begingroup$
That curve is not a circle (or rather, that region is not a disc).
$endgroup$
– Brian Tung
Jan 23 at 21:32
1
1
$begingroup$
If you're stuck, plot some points for various values of $theta$ and see if you notice anything
$endgroup$
– pwerth
Jan 23 at 21:32
$begingroup$
If you're stuck, plot some points for various values of $theta$ and see if you notice anything
$endgroup$
– pwerth
Jan 23 at 21:32
$begingroup$
Oh sorry! I meant region instead of circle. I have plotted with desmos several different sin (θ) and also cos (θ), but I can't see a pattern. Only that sin (θ) is shifted upwards with origin (0,1) and cos (θ) to the right at (1,0).
$endgroup$
– d saline
Jan 23 at 21:42
$begingroup$
Oh sorry! I meant region instead of circle. I have plotted with desmos several different sin (θ) and also cos (θ), but I can't see a pattern. Only that sin (θ) is shifted upwards with origin (0,1) and cos (θ) to the right at (1,0).
$endgroup$
– d saline
Jan 23 at 21:42
$begingroup$
Desmos is a good tool to get an idea about the shape of a curve.
$endgroup$
– Math Lover
Jan 23 at 21:48
$begingroup$
Desmos is a good tool to get an idea about the shape of a curve.
$endgroup$
– Math Lover
Jan 23 at 21:48
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
This equation is describing a limacon.
You mention that you have to sketch a circle, but it's not a circle. You can find the drawing corresponding to the equation here.
$r=3+2sin theta$ is an equation that require to use polar coordinates to draw the graph. Be sure to be familiar with it.
Pay attention, in your title you are using "=" but "≤" in your question. "=" will be a line whereas "≤" will be the surface inside that line.
edited Jan 23 at 21:48
gt6989b
34.9k22557
answered Jan 23 at 21:37
Vincent PerezVincent Perez
713
$endgroup$
$begingroup$
Thanks, I have been sloppy with the sign and changed it in the title. That's probably a better way of frasing my question: I don't know ''how'' to plot r ≤ 3+2sin (θ) using polar coordinates. I know that x = rcos (θ), y = rsin (θ), I have tried squaring the term, still can't draw the region.
$endgroup$
– d saline
Jan 24 at 8:41
add a comment |
$begingroup$
Sometimes a picture is worth 1000 words:
If you want to work "by hand," you can make a traditional (rectilinear) plots of $r$, $x$ and $y$ (actually, you only need $x$ and $y$), then sample pairs of coordinates at different $theta$s and transfer them to your polar graph.
answered Jan 23 at 21:45
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
$begingroup$
Thank you, I see I didn't ask my question properly. I know what the region looks like, I just don't know how to draw it by hand without plotting various values of phi.
$endgroup$
– d saline
Jan 24 at 8:36
$begingroup$
I don't think anyone knows how to draw it by hand without plotting various values of $phi$.
$endgroup$
– David G. Stork
Jan 24 at 18:55
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This equation is describing a limacon.
You mention that you have to sketch a circle, but it's not a circle. You can find the drawing corresponding to the equation here.
$r=3+2sin theta$ is an equation that require to use polar coordinates to draw the graph. Be sure to be familiar with it.
Pay attention, in your title you are using "=" but "≤" in your question. "=" will be a line whereas "≤" will be the surface inside that line.
edited Jan 23 at 21:48
gt6989b
34.9k22557
answered Jan 23 at 21:37
Vincent PerezVincent Perez
713
$endgroup$
$begingroup$
Thanks, I have been sloppy with the sign and changed it in the title. That's probably a better way of frasing my question: I don't know ''how'' to plot r ≤ 3+2sin (θ) using polar coordinates. I know that x = rcos (θ), y = rsin (θ), I have tried squaring the term, still can't draw the region.
$endgroup$
– d saline
Jan 24 at 8:41
add a comment |
$begingroup$
This equation is describing a limacon.
You mention that you have to sketch a circle, but it's not a circle. You can find the drawing corresponding to the equation here.
$r=3+2sin theta$ is an equation that require to use polar coordinates to draw the graph. Be sure to be familiar with it.
Pay attention, in your title you are using "=" but "≤" in your question. "=" will be a line whereas "≤" will be the surface inside that line.
edited Jan 23 at 21:48
gt6989b
34.9k22557
answered Jan 23 at 21:37
Vincent PerezVincent Perez
713
$endgroup$
$begingroup$
Thanks, I have been sloppy with the sign and changed it in the title. That's probably a better way of frasing my question: I don't know ''how'' to plot r ≤ 3+2sin (θ) using polar coordinates. I know that x = rcos (θ), y = rsin (θ), I have tried squaring the term, still can't draw the region.
$endgroup$
– d saline
Jan 24 at 8:41
add a comment |
$begingroup$
This equation is describing a limacon.
You mention that you have to sketch a circle, but it's not a circle. You can find the drawing corresponding to the equation here.
$r=3+2sin theta$ is an equation that require to use polar coordinates to draw the graph. Be sure to be familiar with it.
Pay attention, in your title you are using "=" but "≤" in your question. "=" will be a line whereas "≤" will be the surface inside that line.
edited Jan 23 at 21:48
gt6989b
34.9k22557
answered Jan 23 at 21:37
Vincent PerezVincent Perez
713
$endgroup$
This equation is describing a limacon.
You mention that you have to sketch a circle, but it's not a circle. You can find the drawing corresponding to the equation here.
$r=3+2sin theta$ is an equation that require to use polar coordinates to draw the graph. Be sure to be familiar with it.
Pay attention, in your title you are using "=" but "≤" in your question. "=" will be a line whereas "≤" will be the surface inside that line.
edited Jan 23 at 21:48
gt6989b
34.9k22557
answered Jan 23 at 21:37
Vincent PerezVincent Perez
713
edited Jan 23 at 21:48
gt6989b
34.9k22557
edited Jan 23 at 21:48
gt6989b
34.9k22557
edited Jan 23 at 21:48
gt6989b
34.9k22557
34.9k22557
answered Jan 23 at 21:37
Vincent PerezVincent Perez
713
answered Jan 23 at 21:37
Vincent PerezVincent Perez
713
answered Jan 23 at 21:37
Vincent PerezVincent Perez
713
713
$begingroup$
Thanks, I have been sloppy with the sign and changed it in the title. That's probably a better way of frasing my question: I don't know ''how'' to plot r ≤ 3+2sin (θ) using polar coordinates. I know that x = rcos (θ), y = rsin (θ), I have tried squaring the term, still can't draw the region.
$endgroup$
– d saline
Jan 24 at 8:41
add a comment |
$begingroup$
Thanks, I have been sloppy with the sign and changed it in the title. That's probably a better way of frasing my question: I don't know ''how'' to plot r ≤ 3+2sin (θ) using polar coordinates. I know that x = rcos (θ), y = rsin (θ), I have tried squaring the term, still can't draw the region.
$endgroup$
– d saline
Jan 24 at 8:41
$begingroup$
Thanks, I have been sloppy with the sign and changed it in the title. That's probably a better way of frasing my question: I don't know ''how'' to plot r ≤ 3+2sin (θ) using polar coordinates. I know that x = rcos (θ), y = rsin (θ), I have tried squaring the term, still can't draw the region.
$endgroup$
– d saline
Jan 24 at 8:41
$begingroup$
Thanks, I have been sloppy with the sign and changed it in the title. That's probably a better way of frasing my question: I don't know ''how'' to plot r ≤ 3+2sin (θ) using polar coordinates. I know that x = rcos (θ), y = rsin (θ), I have tried squaring the term, still can't draw the region.
$endgroup$
– d saline
Jan 24 at 8:41
add a comment |
$begingroup$
Sometimes a picture is worth 1000 words:
If you want to work "by hand," you can make a traditional (rectilinear) plots of $r$, $x$ and $y$ (actually, you only need $x$ and $y$), then sample pairs of coordinates at different $theta$s and transfer them to your polar graph.
answered Jan 23 at 21:45
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
$begingroup$
Thank you, I see I didn't ask my question properly. I know what the region looks like, I just don't know how to draw it by hand without plotting various values of phi.
$endgroup$
– d saline
Jan 24 at 8:36
$begingroup$
I don't think anyone knows how to draw it by hand without plotting various values of $phi$.
$endgroup$
– David G. Stork
Jan 24 at 18:55
add a comment |
$begingroup$
Sometimes a picture is worth 1000 words:
If you want to work "by hand," you can make a traditional (rectilinear) plots of $r$, $x$ and $y$ (actually, you only need $x$ and $y$), then sample pairs of coordinates at different $theta$s and transfer them to your polar graph.
answered Jan 23 at 21:45
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
$begingroup$
Thank you, I see I didn't ask my question properly. I know what the region looks like, I just don't know how to draw it by hand without plotting various values of phi.
$endgroup$
– d saline
Jan 24 at 8:36
$begingroup$
I don't think anyone knows how to draw it by hand without plotting various values of $phi$.
$endgroup$
– David G. Stork
Jan 24 at 18:55
add a comment |
$begingroup$
Sometimes a picture is worth 1000 words:
If you want to work "by hand," you can make a traditional (rectilinear) plots of $r$, $x$ and $y$ (actually, you only need $x$ and $y$), then sample pairs of coordinates at different $theta$s and transfer them to your polar graph.
answered Jan 23 at 21:45
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
Sometimes a picture is worth 1000 words:
If you want to work "by hand," you can make a traditional (rectilinear) plots of $r$, $x$ and $y$ (actually, you only need $x$ and $y$), then sample pairs of coordinates at different $theta$s and transfer them to your polar graph.
answered Jan 23 at 21:45
David G. StorkDavid G. Stork
11.1k41432
edited Jan 23 at 22:10
answered Jan 23 at 21:45
David G. StorkDavid G. Stork
11.1k41432
answered Jan 23 at 21:45
David G. StorkDavid G. Stork
11.1k41432
answered Jan 23 at 21:45
David G. StorkDavid G. Stork
11.1k41432
11.1k41432
$begingroup$
Thank you, I see I didn't ask my question properly. I know what the region looks like, I just don't know how to draw it by hand without plotting various values of phi.
$endgroup$
– d saline
Jan 24 at 8:36
$begingroup$
I don't think anyone knows how to draw it by hand without plotting various values of $phi$.
$endgroup$
– David G. Stork
Jan 24 at 18:55
add a comment |
$begingroup$
Thank you, I see I didn't ask my question properly. I know what the region looks like, I just don't know how to draw it by hand without plotting various values of phi.
$endgroup$
– d saline
Jan 24 at 8:36
$begingroup$
I don't think anyone knows how to draw it by hand without plotting various values of $phi$.
$endgroup$
– David G. Stork
Jan 24 at 18:55
$begingroup$
Thank you, I see I didn't ask my question properly. I know what the region looks like, I just don't know how to draw it by hand without plotting various values of phi.
$endgroup$
– d saline
Jan 24 at 8:36
$begingroup$
Thank you, I see I didn't ask my question properly. I know what the region looks like, I just don't know how to draw it by hand without plotting various values of phi.
$endgroup$
– d saline
Jan 24 at 8:36
$begingroup$
I don't think anyone knows how to draw it by hand without plotting various values of $phi$.
$endgroup$
– David G. Stork
Jan 24 at 18:55
$begingroup$
I don't think anyone knows how to draw it by hand without plotting various values of $phi$.
$endgroup$
– David G. Stork
Jan 24 at 18:55
add a comment |
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1
$begingroup$
That equation does not define a circle. Why do you say it is a circle?
$endgroup$
– kccu
Jan 23 at 21:32
$begingroup$
That curve is not a circle (or rather, that region is not a disc).
$endgroup$
– Brian Tung
Jan 23 at 21:32
1
$begingroup$
If you're stuck, plot some points for various values of $theta$ and see if you notice anything
$endgroup$
– pwerth
Jan 23 at 21:32
$begingroup$
Oh sorry! I meant region instead of circle. I have plotted with desmos several different sin (θ) and also cos (θ), but I can't see a pattern. Only that sin (θ) is shifted upwards with origin (0,1) and cos (θ) to the right at (1,0).
$endgroup$
– d saline
Jan 23 at 21:42
$begingroup$
Desmos is a good tool to get an idea about the shape of a curve.
$endgroup$
– Math Lover
Jan 23 at 21:48