Question

Express the plane z=x in (a) cylindrical, and (b) spherical coordinates.

Solid Geometry
ANSWERED
asked 2021-05-30

Express the plane \(z=x\) in (a) cylindrical, and (b) spherical coordinates.

Answers (1)

2021-05-31

It is given that \(z=x\)
(a) In the cylindrical coordinates, \(z=z,x=r\cos\theta\)
Hence the equation becomes, \(z=r\sin\theta\)
(b) In the spherical coordinates, \(x=\rho\sin\theta\cos\phi;z=\rho\cos\theta\)
Hence the equation becomes \(\rho\cos\theta=\rho\sin\theta\cos\phi\)
After rearranging the terms, \(\cot\theta=\cos\phi\)

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