$tan (aggregation)


New in version 4.2.

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.

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.

{ $tan: NaN }
{ $tan: null }

{ $tan : Infinity}


{ $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)"

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

"_id" : ObjectId("5c50782193f833234ba90d85"),
"angle_a" : NumberDecimal("53.13010235415597870314438744090659"),
"side_a" : NumberDecimal("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.

$addFields : {
"side_b" : {
$multiply : [
{ $tan : {$degreesToRadians : "$angle_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" : NumberDecimal("53.13010235415597870314438744090659"),
"side_a" : NumberDecimal("3")
"side_b" : NumberDecimal(4.000000000000000000000000000000000") }

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

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