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I need to convert $\rho \sin\phi=2\cos\theta$ in to rectangular form.

Attempt: I tried using those nice properties : $$x=\rho\sin\phi\cos\theta \\y=\rho\sin\phi\sin\theta\\z=\rho\cos\phi$$ and $\rho^2=x^2+y^2+z^2$ and $\cos\phi=\frac{z}{\sqrt{x^2+y^2+z^2}}$. I cannot find a way to get rid of $\rho$'s and the sines and cosines. Any hints please.

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First, note that $x=\rho\sin\phi\cos\theta$. – Cameron Buie Jun 9 '12 at 1:04
up vote 3 down vote accepted

Multiply by $\rho\sin\phi$, and note that $\rho^2\sin^2\phi=x^2+y^2$.

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