Database Manual / Reference / Query Language / Expressions

$asinh (expression operator)

$asinh

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

$asinh has the following syntax:

{ $asinh: <expression> }

$asinh takes any valid expression that resolves to a number.

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

By default $asinh returns values as a double. $asinh 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, $asinh returns null. If the argument resolves to NaN, $asinh returns NaN. If the argument resolves to negative or positive infinity, $asinh returns negative or positive infinity respectively.

ExampleResults

{ $asinh: NaN }

NaN

{ $asinh: null }

null

{ $asinh : Infinity}

Infinity

{ $asinh : -Infinity }

-Infinity

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("1")
}

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

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

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

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("1"),
  "y-coordinate" : Decimal128("50.49898671052621144221476300417157")
}

Since x-coordinate is stored as a 128-bit decimal, the output of $asinh 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("1")
}

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

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

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("1"),
  "y-coordinate" : Decimal128("1.818446459232066823483698963560709")
}

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