Database Manual / Reference / Query Language / Expressions

$tan (expression operator)（表达式运算符）

$tan

Returns the tangent of a value that is measured in radians.返回以弧度为单位测量的值的切线。

$tan has the following syntax:具有以下语法：

{ $tan: <expression> }

$tan takes any valid expression that resolves to a number. If the expression returns a value in degrees, use the $degreesToRadians operator to convert the result to radians.$tan接受任何解析为数字的有效表达式。如果表达式返回以度为单位的值，请使用$degreesToRadians运算符将结果转换为弧度。

By default $tan returns values as a double. $tan can also return values as a 128-bit decimal as long as the <expression> resolves to a 128-bit decimal value.默认情况下，$tan返回double值。只要<expression>解析为128位十进制值，$tan也可以返回128位十进制的值。

For more information on expressions, see Expressions.有关表达式的详细信息，请参阅表达式。

Behavior行为

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, $tan throws an error.如果参数解析为null值或引用缺少的字段，$tan将返回null。如果参数解析为NaN，$tan将返回NaN。如果参数解析为负无穷大或正无穷大，$tan将抛出错误。

Example示例Results结果
{ $tan: NaN }NaN
{ $tan: null }null

{ $tan : Infinity}

or

{ $tan : -Infinity }

Throws an error message resembling the following formatted output:抛出类似以下格式化输出的错误消息：

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

Example示例

Tangent of Value in Degrees以度为单位的正切值

The trigonometry collection contains a document that stores one side and one angle in a right-angle triangle:trigonometry集合包含一个文档，该文档在直角三角形中存储一条边和一个角：

{
  "_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 $addFields pipeline stage.以下聚合操作使用$tan表达式计算angle_a的对侧，并使用$addFields管道阶段将其添加到输入文档中。

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

The $degreesToRadians expression converts the degree value of angle_a to the equivalent value in radians.$degreesToRadians表达式将angle_a的度数值转换为以弧度为单位的等效值。

The command returns the following output:该命令返回以下输出：

{
  "_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 $tan is a 128-bit decimal.由于angle_a和side_a存储为128位十进制，因此$tan的输出是128位十进制。

Tangent of Value in Radians以弧度为单位的正切值

The trigonometry collection contains a document that stores the hypotenuse and one angle in a right-angle triangle:trigonometry集合包含一个文档，该文档存储直角三角形中的斜边和一个角：

{
  "_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 $addFields pipeline stage.以下聚合操作使用$tan表达式计算与angle_a相邻的边，并使用$addFields管道阶段将其添加到输入文档中。

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

The command returns the following output:该命令返回以下输出：

{
  "_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 $tan is a 128-bit decimal.由于angle_a和side_a存储为128位十进制，因此$tan的输出是128位十进制。