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anonymous

  • one year ago

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  1. anonymous
    • one year ago
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    sorry, r = 2cos(phi) is an equation in spherical coordinates where phi is the polar angle, 0 <phi <pi

  2. anonymous
    • one year ago
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    it is an equation of a sphere in spherical coordinates, need it in rectangular coordinates

  3. phi
    • one year ago
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    usually people use rho rather than "r" (and use r for cylindrical coords)

  4. ganeshie8
    • one year ago
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    \(\rho = 2\cos\phi \implies \rho^2=2\rho\cos\phi = 2z\) Next replace \(\rho^2\) by \(x^2+y^2+z^2\) and you're done!

  5. anonymous
    • one year ago
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    My apologies, I am still learning the coordinate systems and standard notation. phi is the polar angle in spherical coordinates which is between zero and pi

  6. ganeshie8
    • one year ago
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    |dw:1439995254724:dw|

  7. ganeshie8
    • one year ago
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    Notice that in below triangle, we have \(z = \rho\cos\phi\) |dw:1439995296915:dw|

  8. anonymous
    • one year ago
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    ganeshie8 thank you for your help. I see now that I can complete the square on z^2 - 2z to get a nice cartesian equation

  9. ganeshie8
    • one year ago
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    \(\rho = 2\cos\phi \implies \rho^2=2\rho\cos\phi = 2z\) replacing \(\rho^2\) by \(x^2+y^2+z^2\) gives \[x^2+y^2+z^2=2z\] that is the cartesian form...

  10. ganeshie8
    • one year ago
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    and yeah you may complete the square for \(z^2-2z\) to get a nicer one :)

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