Database Manual / Reference / Query Language / Expressions

$cos (expression operator)（表达式运算符）

Definition定义

$cos

Returns the cosine of a value that is measured in radians.返回以弧度为单位测量的值的余弦值。

$cos has the following syntax:具有以下语法：

{ $cos: <expression> }

$cos takes any valid expression that resolves to a number. If the expression returns a value in degrees, use the $degreesToRadians operator to convert the result to radians.$cos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 $cos returns values as a double. $cos can also return values as a 128-bit decimal as long as the <expression> resolves to a 128-bit decimal value.默认情况下，$cos返回double值。只要<expression>解析为128位十进制值，$cos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 +/- Infinitynull、NaN和+/- Infinity

If the argument resolves to a value of null or refers to a field that is missing, $cos returns null. If the argument resolves to NaN, $cos returns NaN. If the argument resolves to negative or positive infinity, $cos throws an error.如果参数解析为null值或引用缺少的字段，则$cos返回null。如果参数解析为NaN，则$cos返回NaN。如果参数解析为负无穷大或正无穷大，$cos将抛出错误。

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

{ $cos : Infinity}

or

{ $cos : -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 $cos to -inf, value must in (-inf,inf)"

Example示例

Cosine of Value in Degrees以度为单位的余弦值

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("53.13010235415597870314438744090659"),
  "hypotenuse" : Decimal128("5")
}

The following aggregation operation uses the $cos expression to calculate the side adjacent to angle_a and add it to the input document using the $addFields pipeline stage.以下聚合操作使用$cos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_a" : {
        $multiply : [
          { $cos : {$degreesToRadians : "$angle_a"} },
          "$hypotenuse"
        ]
      }
    }
  }
])

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("2.999999999999999999999999999999999"),
  "hypotenuse" : Decimal128("5"),
}

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

Cosine of Value in Radians以弧度为单位的余弦值

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"),
  "hypotenuse" : Decimal128("5")
}

The following aggregation operation uses the $cos expression to calculate the side adjacent to angle_a and add it to the input document using the $addFields pipeline stage.以下聚合操作使用$cos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 : [
          { $cos : "$angle_a" },
          "$hypotenuse"
        ]
      }
    }
  }
])

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

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "angle_a" : Decimal128("0.9272952180016122324285124629224288"),
  "side_b" : Decimal128("3.000000000000000000000000000000000"),
  "hypotenuse" : Decimal128("5"),
}

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