$acos (aggregation)


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 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.

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.

{ $acos: NaN }
{ $acos: null }

{ $acos : Infinity}


{ $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]"

The trigonometry collection contains a document that stores three sides of a right-angle 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.

$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 128-bit decimals, the output of $acos is a 128-bit decimal.

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