$acosh (aggregation)

• $acosh

New in version 4.2.

Returns the inverse hyperbolic cosine (hyperbolic arc cosine) ofa value.

$acosh has the following syntax:

{ $acosh: <expression> }

$acosh takes any valid expression that resolves to a number between 1and +Infinity, e.g. 1 <= value <= +Infinity.

$acosh returns values in radians. Use$radiansToDegrees operator to convert the output valuefrom radians to degrees.

By default $acosh returns values as a double.$acosh can also return values as a128-bit decimalas long as the <expression> resolves to a 128-bit decimal value.

For more information on expressions, seeExpressions.

Behavior

null, NaN, and +/- Infinity

If the argument resolves to a value of null or refers to a fieldthat is missing, $acosh returns null. If the argumentresolves to NaN, $acosh returns NaN. If theargument resolves to negative infinity, $acosh throws anerror. If the argument resolves to Infinity, $acoshreturns Infinity. If the argument resolves to a value outside thebounds of [-1, Infinity] inclusive, $acosh throws an error.

"errmsg" :  "Failed to optimize pipeline :: caused by :: cannot  apply $acosh to -inf, value must in (1,inf)"

Example

• Inverse Hyperbolic Cosine of Value in Degrees
• Inverse Hyperbolic Cosine of Value in Radians

The trigonometry collection contains a document thatstores a value along the x axis of a 2-D graph:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : NumberDecimal("3")
}

The following aggregation operation uses the$acosh expression to calculate inverse hyperboliccosine of x-coordinate and add it to the input document usingthe $addFields pipeline stage.

db.trigonometry.aggregate([
  {
    $addFields : {
      "y-coordinate" : {
        $radiansToDegrees : { $acosh : "$x-coordinate" }
      }
    }
  }
])

The $radiansToDegrees expression converts theradian value returned by $acosh to the equivalentvalue in degrees.

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : NumberDecimal("3"),
  "y-coordinate" : NumberDecimal("100.9979734210524228844295260083432")
}

Since x-coordinate is stored as a128-bit decimal, the output of$acosh is a 128-bit decimal.

The trigonometry collection contains a document thatstores a value along the x axis of a 2-D graph:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : NumberDecimal("3")
}

The following aggregation operation uses the$acosh expression to calculate inverse hyperboliccosine of x-coordinate and add it to the input document usingthe $addFields pipeline stage.

db.trigonometry.aggregate([
  {
    $addFields : {
      "y-coordinate" : {
        $acosh : "$x-coordinate"
      }
    }
  }
])

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : NumberDecimal("3"),
  "y-coordinate" : NumberDecimal("1.762747174039086050465218649959585")
}

Since x-coordinate is stored as a128-bit decimal, the output of$acosh is a 128-bit decimal.