$atanhReturns the inverse hyperbolic tangent (hyperbolic arc tangent) of a value.
$atanhhas the following syntax:{ $atanh: <expression> }$atanhtakes any valid expression that resolves to a number between-1and1, e.g.-1 <= value <= 1.$atanhreturns values in radians. Use$radiansToDegreesoperator to convert the output value from radians to degrees.By default
$atanhreturns values as adouble.$atanhcan 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, $atanh returns null. If the argument resolves to NaN, $atanh returns NaN. If the argument resolves to negative or positive infinity, $atanh throws an error. If the argument resolves to +1 or -1, $atanh returns Infinity and -Infinity respectively.
Example | Results |
|---|---|
|
|
|
|
|
|
|
|
or
| Throws an error message resembling the following formatted output: |
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("0.5")}The following aggregation operation uses the $atanh expression to calculate inverse hyperbolic tangent of x-coordinate and add it to the input document using the $addFields pipeline stage.
db.trigonometry.aggregate([ { $addFields : { "y-coordinate" : { $radiansToDegrees : { $atanh : "$x-coordinate" } } } }])The $radiansToDegrees expression converts the radian value returned by $atanh to the equivalent value in degrees.
The command returns the following output:
{ "_id" : ObjectId("5c50782193f833234ba90d85"), "x-coordinate" : Decimal128("0.5"), "y-coordinate" : Decimal128("31.47292373094538001977241539068589")}Since x-coordinate is stored as a 128-bit decimal, the output of $atanh 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("0.5")}The following aggregation operation uses the $atanh expression to calculate inverse hyperbolic tangent of x-coordinate and add it to the input document using the $addFields pipeline stage.
db.trigonometry.aggregate([ { $addFields : { "y-coordinate" : { $atanh : "$x-coordinate" } } }])The command returns the following output:
{ "_id" : ObjectId("5c50782193f833234ba90d85"), "x-coordinate" : Decimal128("0.5"), "y-coordinate" : Decimal128("0.5493061443340548456976226184612628")}Since x-coordinate is stored as a 128-bit decimal, the output of $asin is a 128-bit decimal.