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

naivlingr

naivlingr

Answered question

2021-05-30

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

Answer & Explanation

Viktor Wiley

Viktor Wiley

Skilled2021-05-31Added 84 answers

It is given that z=x
(a) In the cylindrical coordinates, z=z,x=rcosθ
Hence the equation becomes, z=rsinθ
(b) In the spherical coordinates, x=ρsinθcosϕ;z=ρcosθ
Hence the equation becomes ρcosθ=ρsinθcosϕ
After rearranging the terms, cotθ=cosϕ

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