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$atan2 (aggregation)

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$atan2

New in version 4.2.

Returns the inverse tangent (arc tangent) of y / x, where y and x are the first and second values passed to the expression respectively.

$atan2 has the following syntax:

{ $atan2: [ <expression 1>, <expression 2> ] }

$atan2 takes any valid expression that resolves to a number.

$atan2 returns values in radians. Use $radiansToDegrees operator to convert the output value from radians to degrees.

By default $atan2 returns values as a double. $atan2 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 and NaN

If the first argument to $atan2 is null, $atan2 returns null. If the first argument to $atan2 is NaN, $atan2 returns NaN. If the first argument resolves to a number and the second argument resolves to either NaN or null, $atan2 returns the NaN or null respectively.

Example Results

{ $atan2: [ NaN, <value> ] }

or

{ $atan2: [ <value>, NaN ] }

NaN

{ $atan2: [ null, <value> ] }

or

{ $atan2: [ <value>, null ] }

null

Example

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

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

The following aggregation operation uses the $atan2 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 : {
          $atan2 : [ "$side_b", "$side_a" ]
        }
      }
    }
  }
])

The $radiansToDegrees expression converts the radian value returned by $atan2 to the equivalent value in degrees.

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : NumberDecimal("3"),
  "side_b" : NumberDecimal("4"),
  "hypotenuse" : NumberDecimal("5"),
  "angle_a" : NumberDecimal("53.13010235415597870314438744090658")
}

Since side_b and side_a are stored as 128-bit decimals, the output of $atan2 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" : NumberDecimal("3"),
  "side_b" : NumberDecimal("4"),
  "hypotenuse" : NumberDecimal("5")
}

The following aggregation operation uses the $atan2 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" : {
        $atan2 : [ "$side_b", "$side_a" ]
      }
    }
  }
])

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : NumberDecimal("3"),
  "side_b" : NumberDecimal("4"),
  "hypotenuse" : NumberDecimal("5"),
  "angle_a" : NumberDecimal("0.9272952180016122324285124629224287")
}

Since side_b and side_a are stored as 128-bit decimals, the output of $atan2 is a 128-bit decimal.