Construct an angle from a number of radians.

Convert an angle to a number of radians.

Construct an angle from a number of degrees.

Angle.degrees 180
--> Angle.radians pi

Convert an angle to a number of degrees.

Angle.turns 2 |> Angle.inDegrees
--> 720

Construct an angle from a number of turns.

Angle.turns -0.25
--> Angle.degrees -90

Convert an angle to a number of turns.

Angle.radians pi |> Angle.inTurns
--> 0.5

Construct an angle from a number of minutes.

Angle.minutes 30
--> Angle.degrees 0.5

Convert an angle to a number of minutes.

Angle.degrees 2 |> Angle.inMinutes
--> 120

Construct an angle from a number of seconds.

Angle.seconds 120
--> Angle.minutes 2

Convert an angle to a number of seconds.

Angle.degrees 0.1 |> Angle.inSeconds
--> 360

The sign of an angle given in degrees, minutes and seconds.

Construct an angle given its sign and its degree, minute and second components. The signs of degrees, minutes and seconds will be ignored (their absolute values will be used). Note that only seconds may be fractional! In general minutes and seconds should each be less than 60, but this is not enforced.

Angle.fromDms
    { sign = Angle.Positive
    , degrees = 45
    , minutes = 30
    , seconds = 36
    }
--> Angle.degrees 45.51


Angle.fromDms
    { sign = Angle.Negative
    , degrees = 2
    , minutes = 15
    , seconds = 0
    }
--> Angle.degrees -2.25

Convert an angle to a number of degrees, minutes and seconds, along with its sign. The degrees, minutes and seconds values will all be non-negative, and both minutes and seconds will be less than 60.

Angle.toDms (Angle.degrees 1.5)
--> { sign = Angle.Positive
--> , degrees = 1
--> , minutes = 30
--> , seconds = 0
--> }


Angle.toDms (Angle.degrees -0.751)
--> { sign = Angle.Negative
--> , degrees = 0
--> , minutes = 45
--> , seconds = 3.6
--> }

You could use this to write a string-conversion function for angles, something like:

angleString angle =
    let
        { sign, degrees, minutes, seconds } =
            Angle.toDms angle


        signString =
            case sign of
                Angle.Positive ->
                    ""


                Angle.Negative ->
                    "-"
    in
    String.concat
        [ signString
        , String.fromInt degrees
        , "° "
        , String.fromInt minutes
        , "′ "
        , Round.round 3 seconds
        , "″"
        ]

(Here we're using the myrho/elm-round package to control the number of decimal places used when displaying the number of seconds.)