Cartesian, Cylindrical, and Spherical Coordinates

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18 Terms

1
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Cylindrical
x =

r cos θ

2
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Cylindrical
y =

r sin θ

3
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Cylindrical
z =

z

4
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Cylindrical
r =

sqrt(x^2 + y^2)

5
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Cylindrical
θ =

arcsin (y / sqrt(x^2 + y^2)

6
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Cylindrical
z =

z

7
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Spherical
x =

ρ sinϕ cosθ

8
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Spherical
y =

ρ sinϕ sinθ

9
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Spherical
z =

ρ cos ϕ

10
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Spherical
ρ =

sqrt(x^2 + y^2 + z^2)

11
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Spherical
θ =

arcsin (y/ sqrt(x^2 + y^2))

12
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Spherical
ϕ =

arcsin (sqrt(x^2 + y^2)/ sqrt(x^2 + y^2 + z^2))

13
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Cylindrical --> Spherical
ρ =

sqrt(r^2 + z^2)

14
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Cylindrical --> Spherical
θ =

θ

15
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Cylindrical --> Spherical
ϕ =

arctan (r / z)

16
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Spherical --> Cylindrical
r =

ρ sin ϕ

17
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Spherical --> Cylindrical
θ =

θ

18
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Spherical --> Cylindrical
z =

ρ cos ϕ