c

Question

c

anonymous · Answer

sorry, r = 2cos(phi) is an equation in spherical coordinates where phi is the polar angle, 0 <phi <pi

anonymous · Answer

it is an equation of a sphere in spherical coordinates, need it in rectangular coordinates

phi · Answer

usually people use rho rather than  "r"  (and use r for cylindrical coords)

ganeshie8 · Answer

$\rho = 2\cos\phi \implies \rho^2=2\rho\cos\phi = 2z$

Next replace $\rho^2$ by $x^2+y^2+z^2$ and you're done!

anonymous · Answer

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 · Answer

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ganeshie8 · Answer

Notice that in below triangle, we have $z = \rho\cos\phi$

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anonymous · Answer

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 · Answer

$\rho = 2\cos\phi \implies \rho^2=2\rho\cos\phi = 2z$

replacing $\rho^2$ by $x^2+y^2+z^2$ gives
$$x^2+y^2+z^2=2z$$

that is the cartesian form...

ganeshie8 · Answer

and yeah you may complete the square for $z^2-2z$ to get a nicer one :)