List of Coordinate Systems Geometry Math Formulas Latex Code

rockingdingo 2023-05-23 #Geometry #Math

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In this blog, we will summarize the latex code for Geometry Coordinate Systems, Math Formulas. Topics include Cartesian to Cylindrical Coordinates, Cartesian to Polar Coordinates, Cartesian to Spherical Coordinates, Cylindrical to Spherical Coordinates, etc.

Coordinate Systems

Cartesian to Cylindrical Coordinates

Cartesian to Polar Coordinates

Cartesian to Spherical Coordinates

Cylindrical to Spherical Coordinates

Coordinate Systems

Cartesian to Cylindrical Coordinates

Math,Geometry

Equation

$\begin{array}{*{20}c} {x = r\cos \theta } & {r = \sqrt {x^2 + y^2 } } & {} \\ {y = r\sin \theta } & {\theta = \tan ^{ - 1} \left( {\frac{y}{x}} \right)} & {} \\ {z = z} & {z = z} & {} \\ \end{array}$

Latex Code

            \begin{array}{*{20}c} {x = r\cos \theta } & {r = \sqrt {x^2 + y^2 } } & {} \\ {y = r\sin \theta } & {\theta = \tan ^{ - 1} \left( {\frac{y}{x}} \right)} & {} \\ {z = z} & {z = z} & {} \\ \end{array}

Explanation

Latex code for Cartesian to Cylindrical Coordinates.

$(x,y,z)$ : Cylindrical Coordinates
$r$ : Radius

Cartesian to Polar Coordinates

Math,Geometry

Equation

$\begin{array}{*{20}c} {x = r\cos \theta } & {r = \sqrt {x^2 + y^2 } } \\ {y = r\sin \theta } & {\theta = \tan ^{ - 1} \left( {\frac{y}{x}} \right)} \\ \end{array}$

Latex Code

            \begin{array}{*{20}c} {x = r\cos \theta } & {r = \sqrt {x^2 + y^2 } } \\ {y = r\sin \theta } & {\theta = \tan ^{ - 1} \left( {\frac{y}{x}} \right)} \\ \end{array}

Explanation

Latex code for Cartesian to Polar Coordinates.

$(x,y)$ : Polar Coordinates
$r$ : Radius

Cartesian to Spherical Coordinates

Math,Geometry

Equation

$\begin{array}{*{20}c} {x = R\sin \theta \cos \phi } & {R = \sqrt {x^2 + y^2 + z^2 } } & {} \\ {y = R\sin \theta \sin \phi } & {\phi = \tan ^{ - 1} \left( {\frac{y}{x}} \right)} & {} \\ {z = R\cos \theta } & {\theta = \cos ^{ - 1} \left( {\frac{z}{{\sqrt {x^2 + y^2 + z^2 } }}} \right)} & {} \\ \end{array}$

Latex Code

            \begin{array}{*{20}c} {x = R\sin \theta \cos \phi } & {R = \sqrt {x^2 + y^2 + z^2 } } & {} \\ {y = R\sin \theta \sin \phi } & {\phi = \tan ^{ - 1} \left( {\frac{y}{x}} \right)} & {} \\ {z = R\cos \theta } & {\theta = \cos ^{ - 1} \left( {\frac{z}{{\sqrt {x^2 + y^2 + z^2 } }}} \right)} & {} \\ \end{array}

Explanation

Latex code for Cartesian to Spherical Coordinates.

$(x,y,z)$ : Spherical Coordinates
$r$ : Radius

Cylindrical to Spherical Coordinates

Math,Geometry

Equation

$\begin{array}{*{20}c} {r = R\sin \theta } & {R = \sqrt {r^2 + z^2 } } & {} \\ {z = R\sin \theta } & {\phi = \theta } & {} \\ {\theta = \phi } & {\theta = \tan ^{ - 1} \left( {\frac{r}{z}} \right)} & {} \\ \end{array}$

Latex Code

            \begin{array}{*{20}c} {r = R\sin \theta } & {R = \sqrt {r^2 + z^2 } } & {} \\ {z = R\sin \theta } & {\phi = \theta } & {} \\ {\theta = \phi } & {\theta = \tan ^{ - 1} \left( {\frac{r}{z}} \right)} & {} \\ \end{array}

Explanation

Latex code for Cylindrical to Spherical Coordinates.

$(x,y,z)$ : Spherical Coordinates
$r$ : Radius

Cartesian to Cylindrical Coordinates

Equation

Latex Code

Explanation

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Cartesian to Polar Coordinates

Equation

Latex Code

Explanation

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Cartesian to Spherical Coordinates

Equation

Latex Code

Explanation

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Cylindrical to Spherical Coordinates

Equation

Latex Code

Explanation

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