Database Manual / Reference / Query Language / Expressions

$acos (expression operator)（表达式运算符）

$acos

Returns the inverse cosine (arc cosine) of a value.返回值的反余弦（弧余弦）。

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

{ $acos: <expression> }

$acos takes any valid expression that resolves to a number between -1 and 1, e.g. -1 <= value <= 1.接受解析为-1到1之间的数字的任何有效表达式，例如-1 <= value <= 1。

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

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

If the argument resolves to a value of null or refers to a field that is missing, $acos returns null. 如果参数解析为null值或引用缺少的字段，则$acos将返回null。If the argument resolves to NaN, $acos returns NaN. 如果参数解析为NaN，$acos将返回NaN。If the argument resolves to a value outside the bounds of [-1, 1] inclusive, $acos throws an error.如果参数解析为[-1, 1]范围之外的值，则$acos将抛出错误。

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

{ $acos : Infinity}

or

{ $acos : -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 $acos to -inf, value must in [-1,1]"

Example示例

Inverse Cosine of Value in Degrees以度为单位的反余弦值

The trigonometry collection contains a document that stores three sides of a right-angle triangle:trigonometry（三角学）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 $acos expression to calculate the angle adjacent to side_a and add it to the input document using the $addFields pipeline stage.以下聚合操作使用$acos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 : {
          $acos : {
            $divide : [ "$side_b", "$hypotenuse" ]
          }
        }
      }
    }
  }
])

The $radiansToDegrees expression converts the radian value returned by $acos to the equivalent value in degrees.$radiansToDegrees表达式将$acos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("36.86989764584402129685561255909341")
}

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

Inverse Cosine of Value in Radians以弧度为单位的反余弦值

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 $acos expression to calculate the angle adjacent to side_a and add it to the input document using the $addFields pipeline stage.以下聚合操作使用$acos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" : {
        $acos : {
          $divide : [ "$side_b", "$hypotenuse" ]
        }
      }
    }
  }
])

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("0.6435011087932843868028092287173226")
}

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