Database Manual / Reference / Query Language / Expressions

$atan (expression operator)

$atan

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

$atan has the following syntax:

{ $atan: <expression> }

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

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

By default $atan returns values as a double. $atan 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 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.

ExampleResults

{ $atan: NaN }

NaN

{ $atan: null }

null

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.