Introduction to MongoDB $tan Operator

$tan is a mathematical operator in MongoDB used to calculate the tangent of a given angle.

Syntax

The syntax for the $tan operator is as follows:

{ $tan: <angle> }

Here, <angle> is a numeric expression that represents the angle whose tangent value needs to be calculated, in radians.

Use Cases

The $tan operator can be used in scenarios that require the calculation of tangent values. For example, in geospatial applications, it can be used to calculate the angle between two geographical locations and, subsequently, their distance.

Example

Assume that there is a locations collection that contains multiple documents, where each document represents a geographical location with longitude and latitude fields, as shown below:

{
  "_id": 1,
  "name": "Shanghai",
  "location": {
    "type": "Point",
    "coordinates": [121.4737, 31.2304]
  }
}

Now, suppose that we need to calculate the angle and distance between Shanghai and Beijing. We can use the $geoNear index and the $tan operator, as shown below:

db.locations.aggregate([
  {
    $geoNear: {
      near: {
        type: "Point",
        coordinates: [116.4074, 39.9042]
      },
      distanceField: "distance",
      spherical: true
    }
  },
  {
    $project: {
      angle: { $tan: { $divide: ["$distance", 6371] } },
      distance: 1
    }
  }
])

This aggregation pipeline uses the $geoNear index to find the location closest to Beijing and then uses the $project operator to calculate the angle and distance. In the $project operator, the $divide operator is used to convert the distance to radians, and then the $tan operator is used to calculate the tangent value. Running the above aggregation pipeline results in a similar output:

{
  "_id": 1,
  "distance": 897.2048198290362,
  "angle": 0.015711567826785733
}

Here, the angle field represents the angle between Shanghai and Beijing in radians, which can be further converted to degrees.

Conclusion

The $tan operator is a commonly used mathematical operator in MongoDB used to calculate the tangent of a given angle. In geospatial applications, it can be used to calculate the angle between two geographical locations and, subsequently, their distance.