The $cos operator computes the cosine of an angle in MongoDB aggregation pipelines. Use it for geometry, signal processing, and physics calculations when your data stores angles in radians.
Angle → ratio.
One expression inside $cos.
Input must be radians.
Always -1 to 1.
Geometry, signals, physics.
Forward vs inverse.
In MongoDB’s aggregation framework, the $cos operator returns the cosine of a numeric angle expressed in radians. For example, cos(0) = 1 and cos(π/2) = 0. The result is always between -1 and 1.
$cos expects radians, not degrees. If your data stores degrees, convert first with $multiply and $divide before applying $cos.
The $cos operator takes one numeric expression (angle in radians):
{ $cos: <expression> }$cos — returns the cosine of the angle in radians.<expression> — a field reference, literal, or nested numeric expression.-1 to 1 (inclusive).$project, $addFields, or $set.null, the result is null.radians = degrees × (π / 180)$acos($cos(x)) ≈ x within the valid domain| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (trigonometry) |
| Syntax | { $cos: <expression> } |
| Input unit | Radians (any real number) |
| Output range | -1 to 1 |
| Common stages | $project, $addFields, $set |
{
$cos: 0
}Returns 1
{
$cos: "$radians"
}Cosine of angle field
{
$cos: 1.5707963267948966
}Returns 0 (90°)
{
$cos: null
}Returns null
Compute cosines from stored radian values, convert degrees first, and explore common boundary angles with $cos.
Use an angles collection with radian measurements and compute cosine with $project.
Suppose you have an angles collection where each document stores an angle in radians:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "radians": 0 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "radians": 1 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "radians": 2 }
]Compute the cosine of each stored angle:
db.angles.aggregate([
{
$project: {
radians: 1,
cosine: { $cos: "$radians" }
}
}
])radians: 0 → cos(0) = 1radians: 1 → cos(1) ≈ 0.5403radians: 2 → cos(2) ≈ -0.4161Convert degrees to radians, compute x-components on the unit circle, and handle common boundary values.
When your data stores degrees, convert before applying $cos:
db.angles.aggregate([
{
$project: {
degrees: 1,
cosine: {
$cos: {
$multiply: [
"$degrees",
{ $divide: [ 3.141592653589793, 180 ] }
]
}
}
}
}
])
// degrees: 60 → cosine ≈ 0.5
// degrees: 90 → cosine ≈ 0
// degrees: 180 → cosine ≈ -1The formula is radians = degrees × (π / 180). Nest the conversion inside $cos so the pipeline handles everything in one stage.
On a unit circle, the x-coordinate equals cos(θ). Compute it from a stored angle:
db.vectors.aggregate([
{
$project: {
label: 1,
angleRadians: 1,
xComponent: { $cos: "$angleRadians" },
yComponent: { $sin: "$angleRadians" }
}
}
])Pair $cos with $sin to recover both coordinates from an angle. This pattern appears in robotics, game physics, and circular motion models.
Common boundary values every beginner should know:
db.samples.aggregate([
{
$project: {
cosZero: { $cos: 0 }, // 1
cosPi2: { $cos: 1.5707963267948966 }, // ≈ 0 (π/2)
cosPi: { $cos: 3.141592653589793 }, // ≈ -1 (π)
cosTwoPi: { $cos: 6.283185307179586 } // ≈ 1 (2π)
}
}
])$cos(0) = 1, $cos(π/2) = 0, and $cos(π) = -1. These edge cases help validate pipeline logic and unit tests.
$cos WorksThe pipeline evaluates the input — a field like "$radians" or a numeric expression in radians.
MongoDB computes cos(angle) and returns a value between -1 and 1.
The cosine value is written to the field you define in $project or $addFields.
Use in further math, pair with $sin, or feed into inverse ops like $acos.
The $cos operator brings standard cosine math directly into MongoDB aggregation pipelines. Remember that input angles must be in radians, and the output always falls between -1 and 1.
For geometry and physics workloads, pair $cos with $sin to recover full coordinates. Use $acos when you need the inverse — converting a cosine value back to an angle.
$cos$sin for full unit-circle coordinates-1 and 1$acos for the inverse when recovering angles$cos without conversion$cos (angle → ratio) with $acos (ratio → angle)null input returns null$cos (trig) with $cosh (hyperbolic cosine)$cosUse these points when computing cosines in MongoDB.
Angle → ratio.
PurposeOne expression.
SyntaxNot degrees.
RuleOutput range.
PropertyForward vs inverse.
ImportantMove on to $cosh for hyperbolic cosine, or review $convert for type conversion.
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