# Working with Angles¶

The angular components of the various coordinate objects are represented by objects of the Angle class. While most likely to be encountered in the context of coordinate objects, Angle objects can also be used on their own wherever a representation of an angle is needed.

## Creation¶

The creation of an Angle object is quite flexible and supports a wide variety of input object types and formats. The type of the input angle(s) can be array, scalar, tuple, string, Quantity or another Angle. This is best illustrated with a number of examples of valid ways to create an Angle.

### Examples¶

There are a number of ways to create an Angle:

>>> import numpy as np
>>> from astropy import units as u
>>> from astropy.coordinates import Angle

>>> Angle('10.2345d')              # String with 'd' abbreviation for degrees
<Angle 10.2345 deg>
>>> Angle(['10.2345d', '-20d'])    # Array of strings
<Angle [ 10.2345, -20.    ] deg>
>>> Angle('1:2:30.43 degrees')     # Sexagesimal degrees
<Angle 1.04178611 deg>
>>> Angle('1 2 0 hours')           # Sexagesimal hours
<Angle 1.03333333 hourangle>
>>> Angle(np.arange(1., 8.), unit=u.deg)  # Numpy array from 1..7 in degrees
<Angle [1., 2., 3., 4., 5., 6., 7.] deg>
>>> Angle('1°2′3″')               # Unicode degree, arcmin and arcsec symbols
<Angle 1.03416667 deg>
>>> Angle('1°2′3″N')               # Unicode degree, arcmin, arcsec symbols and direction
<Angle 1.03416667 deg>
>>> Angle('1d2m3.4s')              # Degree, arcmin, arcsec.
<Angle 1.03427778 deg>
>>> Angle('1d2m3.4sS')              # Degree, arcmin, arcsec, direction.
<Angle -1.03427778 deg>
>>> Angle('-1h2m3s')               # Hour, minute, second
<Angle -1.03416667 hourangle>
>>> Angle('-1h2m3sW')               # Hour, minute, second, direction
<Angle 1.03416667 hourangle>
>>> Angle((-1, 2, 3), unit=u.deg)  # (degree, arcmin, arcsec)
<Angle -1.03416667 deg>
>>> Angle(10.2345 * u.deg)         # From a Quantity object in degrees
<Angle 10.2345 deg>
>>> Angle(Angle(10.2345 * u.deg))  # From another Angle object
<Angle 10.2345 deg>


## Representation¶

The Angle object also supports a variety of ways of representing the value of the angle, both as a floating point number and as a string.

### Examples¶

There are many ways to represent the value of an Angle:

>>> a = Angle(1, u.radian)
>>> a
1.0
>>> a.degree
57.29577951308232
>>> a.hour
3.8197186342054885
>>> a.hms
hms_tuple(h=3.0, m=49.0, s=10.987083139758766)
>>> a.dms
dms_tuple(d=57.0, m=17.0, s=44.806247096362313)
>>> a.signed_dms
signed_dms_tuple(sign=1.0, d=57.0, m=17.0, s=44.806247096362313)
>>> (-a).dms
dms_tuple(d=-57.0, m=-17.0, s=-44.806247096362313)
>>> (-a).signed_dms
signed_dms_tuple(sign=-1.0, d=57.0, m=17.0, s=44.806247096362313)
>>> a.arcminute
3437.7467707849396
>>> a.to_string()
>>> a.to_string(unit=u.degree)
'57d17m44.8062s'
>>> a.to_string(unit=u.degree, sep=':')
'57:17:44.8062'
>>> a.to_string(unit=u.degree, sep=('deg', 'm', 's'))
'57deg17m44.8062s'
>>> a.to_string(unit=u.hour)
'3h49m10.9871s'
>>> a.to_string(unit=u.hour, decimal=True)
'3.81972'


## Usage¶

Angles will also behave correctly for appropriate arithmetic operations.

### Example¶

To use Angle objects in arithmetic operations:

>>> a = Angle(1.0, u.radian)
>>> a + 0.5 * u.radian + 2 * a
>>> np.sin(a / 2)
<Quantity 0.47942554>
>>> a == a
array(True, dtype=bool)
>>> a == (a + a)
array(False, dtype=bool)


Angle objects can also be used for creating coordinate objects.

### Example¶

To create a coordinate object using an Angle:

>>> from astropy.coordinates import ICRS
>>> ICRS(Angle(1, u.deg), Angle(0.5, u.deg))
<ICRS Coordinate: (ra, dec) in deg
(1., 0.5)>


## Wrapping and Bounds¶

There are two utility methods for working with angles that should have bounds. The wrap_at() method allows taking an angle or angles and wrapping to be within a single 360 degree slice. The is_within_bounds() method returns a boolean indicating whether an angle or angles is within the specified bounds.

## Longitude and Latitude Objects¶

Longitude and Latitude are two specialized subclasses of the Angle class that are used for all of the spherical coordinate classes. Longitude is used to represent values like right ascension, Galactic longitude, and azimuth (for Equatorial, Galactic, and Alt-Az coordinates, respectively). Latitude is used for declination, Galactic latitude, and elevation.

### Longitude¶

A Longitude object is distinguished from a pure Angle by virtue of a wrap_angle property. The wrap_angle specifies that all angle values represented by the object will be in the range:

wrap_angle - 360 * u.deg <= angle(s) < wrap_angle


The default wrap_angle is 360 deg. Setting 'wrap_angle=180 * u.deg' would instead result in values between -180 and +180 deg. Setting the wrap_angle attribute of an existing Longitude object will result in re-wrapping the angle values in-place. For example:

>>> from astropy.coordinates import Longitude
>>> a = Longitude([-20, 150, 350, 360] * u.deg)
>>> a.degree
array([340., 150., 350.,   0.])
>>> a.wrap_angle = 180 * u.deg
>>> a.degree
array([-20., 150., -10.,   0.])


### Latitude¶

A Latitude object is distinguished from a pure Angle by virtue of being bounded so that:

-90.0 * u.deg <= angle(s) <= +90.0 * u.deg


Any attempt to set a value outside of that range will result in a ValueError.