$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.

Example	Results
`{ $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.

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$acosh