$acos (aggregation)

  • $acos

New in version 4.2.

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

$acos has the following syntax:

  1. { $acos: <expression> }

$acos takes any valid expression that resolves to a number between -1and 1, e.g. -1 <= value <= 1.

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

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

If the argument resolves to a value of null or refers to a fieldthat is missing, $acos returns null. If theargument resolves to NaN, $acos returns NaN.If the argument resolves to a value outside the bounds of[-1, 1] inclusive, $acos throws an error.

ExampleResults
{ $acos: NaN }NaN
{ $acos: null }null
{ $acos : Infinity}or{ $acos : -Infinity }Throws an error message resembling the following formattedoutput:
  1. "errmsg" :  "Failed to optimize pipeline :: caused by :: cannot  apply $acos to -inf, value must in [-1,1]"

Example

  • Inverse Cosine of Value in Degrees
  • Inverse Cosine 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$acos expression to calculate the angle adjacentto side_a and add it to the input document using the$addFields pipeline stage.

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

The $radiansToDegrees expression converts theradian value returned by $acos 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("36.86989764584402129685561255909341")
  7. }

Since side_b and hypotenuse are stored as128-bit decimals, the output of$acos 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$acos expression to calculate the angle adjacentto side_a and add it to the input document using the$addFields pipeline stage.

  1. db.trigonometry.aggregate([
  2.   {
  3.     $addFields : {
  4.       "angle_a" : {
  5.         $acos : {
  6.           $divide : [ "$side_b", "$hypotenuse" ]
  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("0.6435011087932843868028092287173226")
  7. }

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