anonymous
  • anonymous
c
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
sorry, r = 2cos(phi) is an equation in spherical coordinates where phi is the polar angle, 0
anonymous
  • anonymous
it is an equation of a sphere in spherical coordinates, need it in rectangular coordinates
phi
  • phi
usually people use rho rather than "r" (and use r for cylindrical coords)

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ganeshie8
  • ganeshie8
\(\rho = 2\cos\phi \implies \rho^2=2\rho\cos\phi = 2z\) Next replace \(\rho^2\) by \(x^2+y^2+z^2\) and you're done!
anonymous
  • anonymous
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
ganeshie8
  • ganeshie8
|dw:1439995254724:dw|
ganeshie8
  • ganeshie8
Notice that in below triangle, we have \(z = \rho\cos\phi\) |dw:1439995296915:dw|
anonymous
  • anonymous
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
ganeshie8
  • ganeshie8
\(\rho = 2\cos\phi \implies \rho^2=2\rho\cos\phi = 2z\) replacing \(\rho^2\) by \(x^2+y^2+z^2\) gives \[x^2+y^2+z^2=2z\] that is the cartesian form...
ganeshie8
  • ganeshie8
and yeah you may complete the square for \(z^2-2z\) to get a nicer one :)

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