The $sin operator computes the sine 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 $sin.
Input must be radians.
Always -1 to 1.
Geometry, signals, physics.
Forward vs inverse.
In MongoDB’s aggregation framework, the $sin operator returns the sine of a numeric angle expressed in radians. For example, sin(0) = 0, sin(π/2) = 1, and sin(π/6) = 0.5 (30°). The result is always between -1 and 1.
$sin expects radians, not degrees. Convert with $degreesToRadians or multiply by π / 180 before applying $sin.
The $sin operator takes one numeric expression (angle in radians):
{ $sin: <expression> }$sin — returns the sine 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) or use $degreesToRadians$asin($sin(x)) ≈ x within the valid domain| Question | Answer |
|---|---|
| Operator type | Aggregation expression operator (trigonometry) |
| Syntax | { $sin: <expression> } |
| Input unit | Radians (any real number) |
| Output range | -1 to 1 |
| Common stages | $project, $addFields, $set |
{
$sin: 0
}Returns 0
{
$sin: "$radians"
}Sine of angle field
{
$sin: 1.5707963267948966
}Returns 1 (90°)
{
$sin: {
$degreesToRadians: 30
}
}Returns 0.5
Compute sines from stored degree values, convert with $degreesToRadians, and explore common boundary angles with $sin.
Use an angles collection with degree measurements and compute sine with $degreesToRadians.
Suppose you have an angles collection where each document stores an angle in degrees:
[
{ "_id": ObjectId("609c26812e9274a86871bc6a"), "degrees": 30 },
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "degrees": 45 },
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "degrees": 60 }
]Convert each angle to radians, then compute its sine:
db.angles.aggregate([
{
$project: {
degrees: 1,
radians: { $degreesToRadians: "$degrees" },
sine: {
$sin: { $degreesToRadians: "$degrees" }
}
}
}
])$degreesToRadians converts the degree field to radians.$sin computes the sine of that radian value.Work with radian fields, recover unit-circle coordinates, and validate boundary values.
When data is already stored in radians, apply $sin directly:
db.angles.aggregate([
{
$project: {
radians: 1,
sine: { $sin: "$radians" }
}
}
])
// radians: 0 → sine: 0
// radians: 1 → sine: ≈ 0.8415
// radians: 1.57 → sine: ≈ 1Skip conversion when your collection already uses radians. This is common in physics and engineering datasets.
On a unit circle, the y-coordinate equals sin(θ). Compute it from a stored angle:
db.vectors.aggregate([
{
$project: {
label: 1,
angleRadians: 1,
xComponent: { $cos: "$angleRadians" },
yComponent: { $sin: "$angleRadians" }
}
}
])Pair $sin with $cos 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: {
sinZero: { $sin: 0 }, // 0
sinPi6: { $sin: 0.5235987755982988 }, // ≈ 0.5 (π/6 = 30°)
sinPi2: { $sin: 1.5707963267948966 }, // ≈ 1 (π/2 = 90°)
sinPi: { $sin: 3.141592653589793 } // ≈ 0 (π = 180°)
}
}
])$sin(0) = 0, $sin(π/2) = 1, and $sin(π) = 0. These edge cases help validate pipeline logic and unit tests.
$sin WorksThe pipeline evaluates the input — a field like "$radians" or a converted degree value in radians.
MongoDB computes sin(angle) and returns a value between -1 and 1.
The sine value is written to the field you define in $project or $addFields.
Use in further math, pair with $cos, or feed into inverse ops like $asin.
The $sin operator brings standard sine 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 $sin with $cos to recover full coordinates. Use $degreesToRadians when your data stores degrees. Next in the series: $sinh.
$degreesToRadians$cos for full unit-circle coordinates-1 and 1$asin for the inverse when recovering angles$sin without conversion$sin (angle → ratio) with $asin (ratio → angle)null input returns null$sin (trig) with $sinh (hyperbolic sine)$sinUse these points when computing sines in MongoDB.
Angle → ratio.
PurposeOne expression.
SyntaxNot degrees.
RuleOutput range.
PropertyForward vs inverse.
ImportantMove on to $sinh for hyperbolic sine, or review $degreesToRadians for angle conversion.
5 people found this page helpful