PolarForm

PolarForm[ v ] converts a vector to polar form.

Usages

`PolarForm[ v ]`

PolarForm[ v ] writes the two-dimensional vector v as a polar vector: magnitude and angle. The angle is exact and in radians. v can be a column vector, a vector in basis form or a coordinate. In a script, wrap the command in Simplify.

Example	in	rendered
A column vector.	`Simplify[ PolarForm[ CartesianVector[3, 4] ] ]`	$\left(5, \tan^{-1}\left(\frac{4}{3}\right)\right)$
A standard angle.	`Simplify[ PolarForm[ CartesianVector[1, 1] ] ]`	$\left(\sqrt{2}, \frac{1}{4}\pi\right)$
A vector along the vertical axis.	`Simplify[ PolarForm[ CartesianVector[0, 2] ] ]`	$\left(2, \frac{1}{2}\pi\right)$
A vector in basis form.	`Simplify[ PolarForm[ BaseVector[3, 4] ] ]`	$\left(5, \tan^{-1}\left(\frac{4}{3}\right)\right)$

Options

`AnglePrecision`

Calculates the angle as a decimal number, rounded to n decimals.

Syntax	Example	rendered
`PolarForm[ v, AnglePrecision=>n ]`	`Simplify[ PolarForm[ CartesianVector[12, 5], AnglePrecision=>2 ] ]`	$\left(13, 0.39\right)$

`MagnitudePrecision`

Calculates the magnitude as a decimal number, rounded to n decimals. Can be combined with AnglePrecision.

Syntax	Example
`PolarForm[ v, MagnitudePrecision=>n ]`	`Simplify[ PolarForm[ CartesianVector[11, 5], AnglePrecision=>2, MagnitudePrecision=>2 ] ]`

Details

Without Simplify, the command is not calculated.
Three dimensions: only two-dimensional vectors are supported: PolarForm[ CartesianVector[3, 4, 5] ] is not calculated.
A vector that is already in polar form is not changed.

See also: ComponentForm, Magnitude, PolarVector