Cot¶

Overview¶

The Cot expression computes the cotangent of a numeric value. It calculates the reciprocal of the tangent function, mathematically equivalent to 1/tan(x) or cos(x)/sin(x).

Syntax¶

COT(expr)

// DataFrame API
import org.apache.spark.sql.functions._
df.select(expr("COT(column_name)"))

Arguments¶

Argument	Type	Description
expr	Numeric	The input value in radians for which to compute the cotangent

Return Type¶

DoubleType - Returns a double-precision floating-point number.

Supported Data Types¶

Numeric types (IntegerType, LongType, FloatType, DoubleType, DecimalType)
Input values are automatically cast to Double for computation

Algorithm¶

Takes the input numeric value as radians
Computes the tangent using math.tan(x)
Calculates the reciprocal: 1 / math.tan(x)
Returns the result as a Double value
Supports Catalyst code generation for optimized execution

Partitioning Behavior¶

How this expression affects partitioning:

Preserves partitioning as it operates on individual row values
Does not require shuffle operations
Can be pushed down to individual partitions for parallel execution

Edge Cases¶

Null handling: Returns null if input is null
Zero tangent: Returns positive or negative infinity when tan(x) = 0 (e.g., at multiples of π)
Overflow behavior: May return Double.PositiveInfinity or Double.NegativeInfinity for certain inputs
NaN handling: Returns NaN for invalid mathematical operations

Code Generation¶

This expression supports Catalyst code generation (Tungsten). The doGenCode method generates optimized Java bytecode using java.lang.Math.tan() for better performance compared to interpreted execution.

Examples¶

-- Basic cotangent calculation
SELECT COT(1);
-- Result: 0.6420926159343306

-- Using with PI for known values
SELECT COT(PI()/4);
-- Result: 1.0 (cotangent of 45 degrees)

-- Cotangent of PI/2 approaches infinity
SELECT COT(PI()/2);
-- Result: 6.123233995736766E-17 (very close to 0, tan(π/2) approaches infinity)

// DataFrame API usage
import org.apache.spark.sql.functions._

val df = Seq(1.0, Math.PI/4, Math.PI/2).toDF("angle")
df.select(col("angle"), expr("COT(angle)").as("cotangent")).show()

// Using with mathematical expressions
df.select(expr("COT(PI()/6)").as("cot_30_degrees")).show()