Given the spherical equation ρ=2cosθsinΦ. Write the equation in rectangular coordinates.

Thanks!!

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- Sep 19th 2009, 04:34 AMjffyxSpherical to Rectangular
Given the spherical equation ρ=2cosθsinΦ. Write the equation in rectangular coordinates.

Thanks!! - Sep 19th 2009, 05:34 AMskeeter
$\displaystyle \rho = 2\cos{\theta}\sin{\phi}$

$\displaystyle \rho^2 = 2\rho \cos{\theta}\sin{\phi}$

... since $\displaystyle x = \rho \sin{\phi} \cos{\theta}$ ...

$\displaystyle \rho^2 = 2x$

... since $\displaystyle \rho = \sqrt{x^2+y^2+z^2}$ ...

$\displaystyle x^2+y^2+z^2 = 2x$

nice website explains it very well ...

Spherical Coordinates