Database Manual / Reference / Query Language / Expressions

$atan (expression operator)（表达式运算符）

$atan

Returns the inverse tangent (arc tangent) of a value.返回值的反正切（反正切）。

$atan has the following syntax:具有以下语法：

{ $atan: <expression> }

$atan takes any valid expression that resolves to a number.接受解析为数字的任何有效表达式。

$atan returns values in radians. Use $radiansToDegrees operator to convert the output value from radians to degrees.返回以弧度为单位的值。使用$radiansToDegrees运算符将输出值从弧度转换为度数。

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

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 and 和NaN

If the argument resolves to a value of null or refers to a field that is missing, $atan returns null. 如果参数解析为null值或引用缺少的字段，$atan将返回null。If the argument resolves to NaN, $tan returns NaN.如果参数解析为NaN，$tan将返回NaN。

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

Example示例

Inverse Tangent of Value in Degrees以度为单位的值的反余切

The trigonometry collection contains a document that stores three sides of a right-angle triangle:trigonometry集合包含一个存储直角三角形三条边的文档：

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5")
}

The following aggregation operation uses the $atan expression to calculate the angle adjacent to side_a and add it to the input document using the $addFields pipeline stage.以下聚合操作使用$atan表达式计算与side_a相邻的角度，并使用$addFields管道阶段将其添加到输入文档中。

db.trigonometry.aggregate([
  {
    $addFields : {
      "angle_a" : {
        $radiansToDegrees : {
          $atan : {
            $divide : [ "$side_b", "$side_a" ]
          }
        }
      }
    }
  }
])

The $radiansToDegrees expression converts the radian value returned by $atan to the equivalent value in degrees.$radiansToDegrees表达式将$atan返回的弧度值转换为以度为单位的等效值。

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

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5"),
  "angle_a" : Decimal128("53.13010235415597870314438744090658")
}

Since side_b and side_a are stored as 128-bit decimals, the output of $atan is a 128-bit decimal.由于side_b和side_a存储为128位十进制，因此$atan的输出是128位十进制。

Inverse Tangent of Value in Radians以弧度为单位的值的反余切

The trigonometry collection contains a document that stores three sides of a right-angle triangle:trigonometry集合包含一个存储直角三角形三条边的文档：

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5")
}

The following aggregation operation uses the $atan expression to calculate the angle adjacent to side_a and add it to the input document using the $addFields pipeline stage.以下聚合操作使用$atan表达式计算与side_a相邻的角度，并使用$addFields管道阶段将其添加到输入文档中。

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

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

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5"),
  "angle_a" : Decimal128("0.9272952180016122324285124629224287")
}

Since side_b and side_a are stored as 128-bit decimals, the output of $atan is a 128-bit decimal.由于side_b和side_a存储为128位十进制，因此$atan的输出是128位十进制。