In MongoDB, the $acos aggregation pipeline operator returns the arccosine (inverse cosine) of a value, measured in radians.

$acos accepts any valid expression that resolves to a number between -1 and 1.

The $acos operator was introduced in MongoDB 4.2.

Example

Suppose we have a collection called test with the following document:

{ "_id" : 1, "data" : 0.5 }

We can use the $acos operator to return the arccosine of the data field:

db.test.aggregate(
  [
    { $project: { 
        _id: 0,
        arccosine: { $acos: "$data" }
      }
    }
  ]
)

Result:

{ "arccosine" : 1.0471975511965976 }

By default, the $acos operator returns values as a double, but it can also return values as a 128-bit decimal as long as the expression resolves to a 128-bit decimal value.

Pi

Providing -1 resolves to the mathematical constant pi (π).

Suppose we add the following document to our collection, which contains a data value of -1.

{ "_id" : 2, "data" : -1 }

Now let’s run the $acos operator against that field:

db.test.aggregate(
  [
    { $match: { _id: 2 } },
    { $project: { 
        _id: 0,
        arccosine: { $acos: "$data" }
      }
    }
  ]
)

Result:

{ "arccosine" : 3.141592653589793 }

This result is π to 15 decimal places.

Convert to Degrees

As mentioned, $acos returns its result in radians. You can use the $radiansToDegrees operator if you want the result in degrees.

Example:

db.test.aggregate(
  [
    { $match: { _id: 2 } },
    { $project: { 
        _id: 0,
        radians: { $acos: "$data" },
        degrees: { $radiansToDegrees: { $acos: "$data" } }
      }
    }
  ]
)

Result:

{ "radians" : 3.141592653589793, "degrees" : 180 }

In this example, the first field presents the result in radians, and the second field presents it in degrees.

Null Values

Null values return null when using the $acos operator.

Suppose we add the following document to our collection:

{ "_id" : 3, "data" : null }

Let’s run the the $acos operator against that document:

db.test.aggregate(
  [
    { $match: { _id: 3 } },
    { $project: { 
        _id: 0,
        arccosine: { $acos: "$data" }
      }
    }
  ]
)

Result:

{ "arccosine" : null }

We can see that the result is null.

NaN Values

If the argument resolves to NaN, $acos returns NaN.

Example:

db.test.aggregate(
  [
    { $match: { _id: 3 } },
    { $project: { 
        _id: 0,
        arccosine: { $acos: 1 * "oops!" }
      }
    }
  ]
)

Result:

{ "arccosine" : NaN }

In this case I tried to multiple a number by a string, which resulted in NaN being returned.

Infinity

If the argument resolves to Infinity or -Infinity, the $acos operator returns an error.

Suppose we add the following document to our collection:

{ "_id" : 4, "data" : Infinity }

Let’s run $acos against the data field:

db.test.aggregate(
  [
    { $match: { _id: 4 } },
    { $project: { 
        _id: 0,
        arccosine: { $acos: "$data" }
      }
    }
  ]
)

Result:

uncaught exception: Error: command failed: {
	"ok" : 0,
	"errmsg" : "cannot apply $acos to inf, value must in [-1,1]",
	"code" : 50989,
	"codeName" : "Location50989"
} : aggregate failed :
_getErrorWithCode@src/mongo/shell/utils.js:25:13
doassert@src/mongo/shell/assert.js:18:14
_assertCommandWorked@src/mongo/shell/assert.js:618:17
assert.commandWorked@src/mongo/shell/assert.js:708:16
DB.prototype._runAggregate@src/mongo/shell/db.js:266:5
DBCollection.prototype.aggregate@src/mongo/shell/collection.js:1046:12
@(shell):1:1

That’s the error I get in the mongo shell when running that code.

Non-Existent Fields

If the $acos operator is applied against a field that doesn’t exist, null is returned.

Example:

db.test.aggregate(
  [
    { $match: { _id: 4 } },
    { $project: { 
        _id: 0,
        arccosine: { $acos: "$oops" }
      }
    }
  ]
)

Result:

{ "arccosine" : null }

Out of Range Values

Providing an out of range value to $acos will result in an error.

Suppose we add the following document to the collection:

{ "_id" : 5, "data" : 2 }

Now let’s run $acos against the data field:

db.test.aggregate(
  [
    { $match: { _id: 5 } },
    { $project: { 
        _id: 0,
        radians: { $acos: "$data" }
      }
    }
  ]
)

Result:

uncaught exception: Error: command failed: {
	"ok" : 0,
	"errmsg" : "cannot apply $acos to 2, value must in [-1,1]",
	"code" : 50989,
	"codeName" : "Location50989"
} : aggregate failed :
_getErrorWithCode@src/mongo/shell/utils.js:25:13
doassert@src/mongo/shell/assert.js:18:14
_assertCommandWorked@src/mongo/shell/assert.js:618:17
assert.commandWorked@src/mongo/shell/assert.js:708:16
DB.prototype._runAggregate@src/mongo/shell/db.js:266:5
DBCollection.prototype.aggregate@src/mongo/shell/collection.js:1046:12
@(shell):1:1

As the error message alludes to, the value must be between -1 and 1.