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# azel2phitheta

Convert angles from azimuth/elevation form to phi/theta form

## Syntax

``PhiTheta = azel2phitheta(AzEl)``

## Description

example

````PhiTheta = azel2phitheta(AzEl)` converts the azimuth/elevation angle pairs to their corresponding phi/theta angle pairs.```

## Examples

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Find the corresponding φ/θ representation for 30° azimuth and 0° elevation.

`PhiTheta = azel2phitheta([30; 0])`
```PhiTheta = 2×1 0 30.0000 ```

## Input Arguments

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Azimuth and elevation angles, specified as a two-row matrix. Each column of the matrix represents an angle in degrees, in the form [azimuth; elevation].

Data Types: `double`

## Output Arguments

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Phi and theta angles, returned as a two-row matrix. Each column of the matrix represents an angle in degrees, in the form [phi; theta]. The matrix dimensions of `PhiTheta` are the same as those of `AzEl`.

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### Azimuth Angle, Elevation Angle

The azimuth angle of a vector is the angle between the x-axis and the orthogonal projection of the vector onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane. These definitions assume the boresight direction is the positive x-axis.

### Note

The elevation angle is sometimes defined in the literature as the angle a vector makes with the positive z-axis. The MATLAB® and Phased Array System Toolbox™ products do not use this definition.

This figure illustrates the azimuth angle and elevation angle for a vector that appears as a green solid line. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue circles. ### Phi Angle, Theta Angle

The φ angle is the angle from the positive y-axis toward the positive z-axis, to the vector’s orthogonal projection onto the yz plane. The φ angle is between 0 and 360 degrees. The θ angle is the angle from the x-axis toward the yz plane, to the vector itself. The θ angle is between 0 and 180 degrees.

The figure illustrates φ and θ for a vector that appears as a green solid line. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue circles. The coordinate transformations between φ/θ and az/el are described by the following equations

`$\begin{array}{l}\mathrm{sin}\left(\text{el}\right)=\mathrm{sin}\varphi \mathrm{sin}\theta \hfill \\ \mathrm{tan}\left(\text{az}\right)=\mathrm{cos}\varphi \mathrm{tan}\theta \hfill \\ \hfill \\ \mathrm{cos}\theta =\mathrm{cos}\left(\text{el}\right)\mathrm{cos}\left(\text{az}\right)\hfill \\ \mathrm{tan}\varphi =\mathrm{tan}\left(\text{el}\right)/\mathrm{sin}\left(\text{az}\right)\hfill \end{array}$`