My Math Forum 3D polar coordinates problem

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 April 17th, 2017, 05:13 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 120 Thanks: 2 3D polar coordinates problem Find the volume below z = r, above the x-y plane, and inside $r= cos \theta$. Answer: 4/9 Is there anyone online tool I could use to plot the 3d polar coordinates? I couldn't approach the problem without any visual clues...
 April 17th, 2017, 06:00 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 680 You can use desmos graphics calculator at https://www.desmos.com/calculator If you click on the wrench icon ("Graph Settings") then "Grid" and click on the polar coordinates icon.
 April 17th, 2017, 06:01 PM #3 Senior Member     Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715 I use the Mathematica function ParametricPlot3D to plot all these things. There is limited access to it at wolframalpha.com You'll have to read up on how to use it. this one is $\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} ~\int_0^{\cos(\theta)} \int_0^r~r~dz~dr~d\theta$
April 18th, 2017, 05:04 PM   #4
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Quote:
 Originally Posted by romsek I use the Mathematica function ParametricPlot3D to plot all these things. There is limited access to it at wolframalpha.com You'll have to read up on how to use it. this one is $\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} ~\int_0^{\cos(\theta)} \int_0^r~r~dz~dr~d\theta$

How did you come up the boundaries (why -pi/2 and pi/2)? It would be great if you could explain a little...

Last edited by zollen; April 18th, 2017 at 05:07 PM.

April 18th, 2017, 05:07 PM   #5
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Quote:
 Originally Posted by zollen How did you come up the boundaries? It would be great if you could explain a little...
do you understand what $r = \cos(\theta)$ is?

and do you understand what

$z = r$ is?

see if you can sketch the first one in 2d and the 2nd one in 3D

April 18th, 2017, 05:10 PM   #6
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I don't know how to plot z=r polar coordinate in 3D...
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April 18th, 2017, 05:12 PM   #7
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Quote:
 Originally Posted by zollen I don't know how to plot z=r polar coordinate in 3D...
bah.

forget about plotting it, can you sketch it? can you at least visualize it?

it's a pretty familiar shape

April 18th, 2017, 05:29 PM   #8
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 April 18th, 2017, 05:38 PM #9 Senior Member   Joined: Jan 2017 From: Toronto Posts: 120 Thanks: 2 Thanks. I am going to study your example closely..
 April 18th, 2017, 05:54 PM #10 Senior Member     Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715 this will probably also help $r = \cos(\theta)$ $r^2 = r \cos(\theta)$ wave the magic wand $x^2 + y^2 = x$ $x^2 - x + y^2 = 0$ $\left(x-\dfrac 1 2\right)^2 +y^2 = \dfrac 1 4$ i.e. circle at $\left( \dfrac 1 2 , 0\right)$ with radius $\dfrac 1 2$ Thanks from topsquark and zollen

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