Rectangular, Cylindrical, Sperical coordinates

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9 Terms

1
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Rectangular

(x,y,z)

2
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Cylindrical

(r,θ,z)

3
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Spherical

(ϕ,θ,ρ)

4
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Rectangular → Cylindrical

r = sqrt(x2 + y2)
θ = arctan(y/x)

z = z

5
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Rectangular → Spherical

ρ = sqrt(x2 + y2 + z2)

θ = arctan(y/x)

ϕ = arccos(z sqrt(x2 + y2 + z2))

6
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Cylindrical → Rectangular

x = r cos(θ)

y = r sin(θ)

z = z

7
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Cylindrical → Spherical

ρ = sqrt(r2 + z2)

θ = θ

ϕ = arctan(r/z)

8
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Spherical → Rectangular

x = ρ sin(ϕ) cos(θ)

y = ρ sin(ϕ) sin(θ)

z = ρ cos(ϕ)

9
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Spherical → Cylindrical

r = ρ sin(ϕ)

θ = θ

z = ρ cos(ϕ)