$atanReturns the inverse tangent (arc tangent) of a value.
$atanhas the following syntax:{ $atan: <expression> }$atantakes any valid expression that resolves to a number.$atanreturns values in radians. Use$radiansToDegreesoperator to convert the output value from radians to degrees.By default
$atanreturns values as adouble.$atancan 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 and NaN
If the argument resolves to a value of null or refers to a field that is missing, $atan returns null. If the argument resolves to NaN, $tan returns NaN.
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Example
The trigonometry collection contains a document that stores three sides of a right-angle triangle:
{ "_id" : ObjectId("5c50782193f833234ba90d85"), "side_a" : Decimal128("3"), "side_b" : Decimal128("4"), "hypotenuse" : Decimal128("5")}The following aggregation operation uses the $atan expression to calculate the angle adjacent to side_a and add it to the input document using the $addFields pipeline stage.
db.trigonometry.aggregate([ { $addFields : { "angle_a" : { $radiansToDegrees : { $atan : { $divide : [ "$side_b", "$side_a" ] } } } } }])The $radiansToDegrees expression converts the radian value returned by $atan to the equivalent value in degrees.
The command returns the following output:
{ "_id" : ObjectId("5c50782193f833234ba90d85"), "side_a" : Decimal128("3"), "side_b" : Decimal128("4"), "hypotenuse" : Decimal128("5"), "angle_a" : Decimal128("53.13010235415597870314438744090658")}Since side_b and side_a are stored as 128-bit decimals, the output of $atan is a 128-bit decimal.
The trigonometry collection contains a document that stores three sides of a right-angle triangle:
{ "_id" : ObjectId("5c50782193f833234ba90d85"), "side_a" : Decimal128("3"), "side_b" : Decimal128("4"), "hypotenuse" : Decimal128("5")}The following aggregation operation uses the $atan expression to calculate the angle adjacent to side_a and add it to the input document using the $addFields pipeline stage.
db.trigonometry.aggregate([ { $addFields : { "angle_a" : { $atan : { $divide : [ "$side_b", "$side_a" ] } } } }])The command returns the following output:
{ "_id" : ObjectId("5c50782193f833234ba90d85"), "side_a" : Decimal128("3"), "side_b" : Decimal128("4"), "hypotenuse" : Decimal128("5"), "angle_a" : Decimal128("0.9272952180016122324285124629224287")}Since side_b and side_a are stored as 128-bit decimals, the output of $atan is a 128-bit decimal.