Database Manual / Reference / Query Language / Expressions

$tan (expression operator)

$tan

Returns the tangent of a value that is measured in radians.

$tan has the following syntax:

{ $tan: <expression> }

$tan takes any valid expression that resolves to a number. If the expression returns a value in degrees, use the $degreesToRadians operator to convert the result to radians.

By default $tan returns values as a double. $tan 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.

Behavior

null, NaN, and +/- Infinity

If the argument resolves to a value of null or refers to a field that is missing, $tan returns null. If the argument resolves to NaN, $tan returns NaN. If the argument resolves to negative or positive infinity, $tan throws an error.

ExampleResults

{ $tan: NaN }

NaN

{ $tan: null }

null

{ $tan : Infinity}

or

{ $tan : -Infinity }

Throws an error message resembling the following formatted output:

"errmsg" :
  "Failed to optimize pipeline :: caused by :: cannot
  apply $tan to -inf, value must in (-inf,inf)"

Example

The trigonometry collection contains a document that stores one side and one angle in a right-angle triangle:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "angle_a" : Decimal128("53.13010235415597870314438744090659"),
  "side_a" : Decimal128("3")
}

The following aggregation operation uses the $tan expression to calculate the side opposite to angle_a and add it to the input document using the $addFields pipeline stage.

db.trigonometry.aggregate([
  {
    $addFields : {
      "side_b" : {
        $multiply : [
          { $tan : {$degreesToRadians : "$angle_a"} },
          "$side_a"
        ]
      }
    }
  }
])

The $degreesToRadians expression converts the degree value of angle_a to the equivalent value in radians.

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "angle_a" : Decimal128("53.13010235415597870314438744090659"),
  "side_a" : Decimal128("3")
  "side_b" : Decimal128("4.000000000000000000000000000000000")
}

Since angle_a and side_a are stored as 128-bit decimals, the output of $tan is a 128-bit decimal.

The trigonometry collection contains a document that stores the hypotenuse and one angle in a right-angle triangle:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "angle_a" : Decimal128("0.9272952180016122324285124629224288"),
  "side_a" : Decimal128("3")
}

The following aggregation operation uses the $tan expression to calculate the side adjacent to angle_a and add it to the input document using the $addFields pipeline stage.

db.trigonometry.aggregate([
  {
    $addFields : {
      "side_b" : {
        $multiply : [
          { $tan : "$angle_a" },
          "$side_a"
        ]
      }
    }
  }
])

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "angle_a" : Decimal128("0.9272952180016122324285124629224288"),
  "side_a" : Decimal128("3")
  "side_b" : Decimal128("3.999999999999999999999999999999999")
}

Since angle_a and side_a are stored as 128-bit decimals, the output of $tan is a 128-bit decimal.