$acos (aggregation)¶
$acos
¶New in version 4.2.
Returns the inverse cosine (arc cosine) of a value.
$acos
has the following syntax:{ $acos: <expression> } $acos
takes any valid expression that resolves to a number between1
and1
, e.g.1 <= value <= 1
.$acos
returns values in radians. Use$radiansToDegrees
operator to convert the output value from radians to degrees.By default
$acos
returns values as adouble
.$acos
can also return values as a 128bit decimal as long as the<expression>
resolves to a 128bit 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  
or
 Throws an error message resembling the following formatted output:

Example¶
The trigonometry
collection contains a document that
stores three sides of a rightangle triangle:
{ "_id" : ObjectId("5c50782193f833234ba90d85"), "side_a" : NumberDecimal("3"), "side_b" : NumberDecimal("4"), "hypotenuse" : NumberDecimal("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" : NumberDecimal("3"), "side_b" : NumberDecimal("4"), "hypotenuse" : NumberDecimal("5"), "angle_a" : NumberDecimal("36.86989764584402129685561255909341") }
Since side_b
and hypotenuse
are stored as
128bit decimals, the output of
$acos
is a 128bit decimal.