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

glucidessho

glucidessho

Answered question

2022-12-19

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

Answer & Explanation

Wayne Underwood

Wayne Underwood

Beginner2022-12-20Added 2 answers

(a) In cylindrical coordinates,
r = r cos θ ,   y = r sin θ ,   z = z
For z=x
z = r cos θ
Belen Booker

Belen Booker

Beginner2022-12-21Added 1 answers

(b) In spherical coordinates,
x = r sin ϕ cos θ ,   y = r sin ϕ sin θ ,   z = r cos ϕ
For z=x
r cos ϕ = r sin ϕ cos θ
r = sin ϕ cos ϕ cos θ = r tan ϕ cos θ
r r tan ϕ cos θ = 0
r ( 1 tan ϕ cos θ ) = 0

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