$atan (aggregation)

  • $atan

New in version 4.2.

Returns the inverse tangent (arc tangent) of a value.

$atan has the following syntax:

  1. { $atan: <expression> }

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

$atan returns values in radians. Use$radiansToDegrees operator to convert the output valuefrom radians to degrees.

By default $atan returns values as a double.$atan can also return values as a128-bit decimalas long as the <expression> resolves to a 128-bit decimal value.

For more information on expressions, seeExpressions.

Behavior

null and NaN

If the argument resolves to a value of null or refers to a fieldthat is missing, $atan returns null. If theargument resolves to NaN, $tan returns NaN.

ExampleResults
{ $atan: NaN }NaN
{ $atan: null }null

Example

  • Inverse Tangent of Value in Degrees
  • Inverse Tangent of Value in Radians

The trigonometry collection contains a document thatstores three sides of a right-angle triangle:

  1. {
  2.   "_id" : ObjectId("5c50782193f833234ba90d85"),
  3.   "side_a" : NumberDecimal("3"),
  4.   "side_b" : NumberDecimal("4"),
  5.   "hypotenuse" : NumberDecimal("5")
  6. }

The following aggregation operation uses the$atan expression to calculate the angle adjacentto side_a and add it to the input document using the$addFields pipeline stage.

  1. db.trigonometry.aggregate([
  2.   {
  3.     $addFields : {
  4.       "angle_a" : {
  5.         $radiansToDegrees : {
  6.           $atan : {
  7.             $divide : [ "$side_b", "$side_a" ]
  8.           }
  9.         }
  10.       }
  11.     }
  12.   }
  13. ])

The $radiansToDegrees expression converts theradian value returned by $atan to the equivalentvalue in degrees.

The command returns the following output:

  1. {
  2.   "_id" : ObjectId("5c50782193f833234ba90d85"),
  3.   "side_a" : NumberDecimal("3"),
  4.   "side_b" : NumberDecimal("4"),
  5.   "hypotenuse" : NumberDecimal("5"),
  6.   "angle_a" : NumberDecimal("53.13010235415597870314438744090658")
  7. }

Since side_b and side_a are stored as128-bit decimals, the output of$atan is a 128-bit decimal.

The trigonometry collection contains a document thatstores three sides of a right-angle triangle:

  1. {
  2.   "_id" : ObjectId("5c50782193f833234ba90d85"),
  3.   "side_a" : NumberDecimal("3"),
  4.   "side_b" : NumberDecimal("4"),
  5.   "hypotenuse" : NumberDecimal("5")
  6. }

The following aggregation operation uses the$atan expression to calculate the angle adjacentto side_a and add it to the input document using the$addFields pipeline stage.

  1. db.trigonometry.aggregate([
  2.   {
  3.     $addFields : {
  4.       "angle_a" : {
  5.         $atan : {
  6.           $divide : [ "$side_b", "$side_a" ]
  7.         }
  8.       }
  9.     }
  10.   }
  11. ])

The command returns the following output:

  1. {
  2.   "_id" : ObjectId("5c50782193f833234ba90d85"),
  3.   "side_a" : NumberDecimal("3"),
  4.   "side_b" : NumberDecimal("4"),
  5.   "hypotenuse" : NumberDecimal("5"),
  6.   "angle_a" : NumberDecimal("0.9272952180016122324285124629224287")
  7. }

Since side_b and side_a are stored as128-bit decimals, the output of$atan is a 128-bit decimal.