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# \$asinh (aggregation).leafygreen-ui-m0pgrr{-webkit-align-self:center;-ms-flex-item-align:center;align-self:center;padding:0 10px;visibility:hidden;}.leafygreen-ui-a30zj9{color:#889397;vertical-align:middle;margin-top:-2px;}.css-1l4s55v{margin-top:-175px;position:absolute;padding-bottom:2px;}

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• Behavior
• Example
\$asinh

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

\$asinh has the following syntax:

 { \$asinh: }

\$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 Expression Operators.

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.

Example
Results
{ \$asinh: NaN }
NaN
{ \$asinh: null }
null
{ \$asinh : Infinity}
Infinity
{ \$asinh : -Infinity }
-Infinity

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

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

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

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