Database Manual / Reference / Query Language / Expressions

$acosh (expression operator)

$acosh

Returns the inverse hyperbolic cosine (hyperbolic arc cosine) of a value.

$acosh has the following syntax:

{ $acosh: <expression> }

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

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

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

For more information on expressions, see Expressions.

Behavior

null, NaN, and +/- Infinity

If the argument resolves to a value of null or refers to a field that is missing, $acosh returns null. If the argument resolves to NaN, $acosh returns NaN. If the argument resolves to negative infinity, $acosh throws an error. If the argument resolves to Infinity, $acosh returns Infinity. If the argument resolves to a value outside the bounds of [-1, Infinity] inclusive, $acosh throws an error.

ExampleResults

{ $acosh: NaN }

NaN

{ $acosh: null }

null

{ $acosh : Infinity}

Infinity

{ $acosh : 0 }

Throws an error message resembling the following formatted output:

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

Example

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

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("3")
}

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

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

The $radiansToDegrees expression converts the radian value returned by $acosh to the equivalent value in degrees.

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("3"),
  "y-coordinate" : Decimal128("100.9979734210524228844295260083432")
}

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

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

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("3")
}

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

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

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("3"),
  "y-coordinate" : Decimal128("1.762747174039086050465218649959585")
}

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