Convert the following equation from spherical to coordinate: sin2(ϕ) + cos2(ϕ)⁄4 = 1/ρ2;
I have converted the right side of the equation to 1/x2+y2+z2, but the fraction on the left side of the equation is throwing me off. Any advice/help/solutions?
2026-03-30 08:21:10.1774858870
Help converting spherical to cartesian?
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$x = \rho\cos\theta\cos\phi\\ y = \rho\sin\theta\cos\phi\\ z = \rho\sin\phi$
$\sin^2\phi + \frac 14 \cos^2\phi = \frac 1{\rho^2}\\ \rho^2\sin^2\phi + \frac 14 \rho^2 \cos^2\phi = 1\\ z^2 + \frac 14 \rho^2 \cos^2\phi = 1$
$x^2+y^2 = \rho^2 \cos^2\phi$
$z^2 + \frac 14 x^2 + \frac 14 y^2 = 1$