Question

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

Solid Geometry

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

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, $$\cot\theta=\cos\phi$$