# AngleVector

AngleVector[θ]

gives the list representing the 2D unit vector at angle θ relative to the axis.

AngleVector[{r,θ}]

gives the list representing the 2D vector of length r at angle θ.

AngleVector[{x,y},θ]

gives the result of starting from the point {x,y}, then going a unit distance at angle θ.

AngleVector[{x,y},{r,θ}]

gives the result of starting from the point {x,y}, then going distance r at angle θ.

# Details

• Unless explicitly given as a Quantity object, the angle θ is assumed to be in radians, counterclockwise starting from the axis. (Multiply by Degree to convert from degrees.)
• AngleVector[{r,θ}] gives a vector that starts at {0,0}.
• The arguments of AngleVector can be symbolic. They can also be Quantity objects.

# Examples

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## Basic Examples(4)

Unit vector at angle θ:

Angles are assumed to be in radians:

Unit vector at angle 30°:

General symbolic case:

## Scope(5)

Unit vector at angle Pi/3:

Use degrees:

Use Quantity angles in input:

Specify the norm of the vector:

Specify the origin of the vector:

Use Quantity values in input:

## Properties & Relations(4)

Reconstruct input:

For short displacements around a geo location, AngleVector approximates GeoDestination:

Move 10 kilometers with initial bearing of 40°:

Re-express that position in terms of a Cartesian frame centered at London:

The horizontal displacement vector in meters is approximately the following:

Folding of AngleVector can be used to move from a point along a sequence of {r,θ} displacements:

The same result can be achieved with AnglePath, using angles relative to the previous segment:

ListPolarPlot can be interpreted as a combination of AngleVector and ListPlot:

ListPolarPlot takes pairs {θi,ri}, but AngleVector takes pairs {r,θ}, so Reverse is needed:

Wolfram Research (2015), AngleVector, Wolfram Language function, https://reference.wolfram.com/language/ref/AngleVector.html.

#### Text

Wolfram Research (2015), AngleVector, Wolfram Language function, https://reference.wolfram.com/language/ref/AngleVector.html.

#### CMS

Wolfram Language. 2015. "AngleVector." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AngleVector.html.

#### APA

Wolfram Language. (2015). AngleVector. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AngleVector.html

#### BibTeX

@misc{reference.wolfram_2024_anglevector, author="Wolfram Research", title="{AngleVector}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/AngleVector.html}", note=[Accessed: 19-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_anglevector, organization={Wolfram Research}, title={AngleVector}, year={2015}, url={https://reference.wolfram.com/language/ref/AngleVector.html}, note=[Accessed: 19-September-2024 ]}