Database Manual / Reference / Query Language / Expressions

$acos (expression operator)

$acos

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

$acos has the following syntax:

{ $acos: <expression> }

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

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

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

If the argument resolves to a value of null or refers to a field that is missing, $acos returns null. If the argument 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 formatted output:

"errmsg" :
  "Failed to optimize pipeline :: caused by :: cannot
  apply $acos to -inf, value must in [-1,1]"

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 $acos 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 : {
          $acos : {
            $divide : [ "$side_b", "$hypotenuse" ]
          }
        }
      }
    }
  }
])

The $radiansToDegrees expression converts the radian value returned by $acos 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("36.86989764584402129685561255909341")
}

Since side_b and hypotenuse are stored as 128-bit decimals, the output of $acos 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 $acos 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" : {
        $acos : {
          $divide : [ "$side_b", "$hypotenuse" ]
        }
      }
    }
  }
])

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5"),
  "angle_a" : Decimal128("0.6435011087932843868028092287173226")
}

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