# How to computes the inverse tangent (arc tangent) of a value using PySpark : trigonometric computations

atan function computes the inverse tangent (arc tangent) of a value, akin to java.lang.Math.atan(). The atan function is particularly useful when dealing with trigonometric computations, common in fields like physics, engineering, and computer graphics. This article delves into the specifics of the atan function in PySpark and provides a hands-on example of its application.

Function signature:

Before we dive into examples, it’s crucial to understand the function signature of `atan`:

``````pyspark.sql.functions.atan(col)
``````

col: The name of the column or an expression that contains the values for which the inverse tangent is to be calculated.

Return value

The `atan` function returns the arc tangent of the input values, which is a floating-point number within the range of -π/2 through π/2.

Example:

Let’s illustrate the use of the `atan` function with a simple example. We’ll create a PySpark DataFrame with hardcoded values, compute their inverse tangent, and display the results.
First, ensure that you have PySpark installed. If not, you can install it using pip:

Sample code
``````from pyspark.sql import SparkSession
from pyspark.sql.functions import atan
from pyspark.sql.types import FloatType
import pyspark.sql.functions as F
# Create a SparkSession
spark = SparkSession.builder \
.appName("PySpark atan example") \
.getOrCreate()

# Sample data
data = [(1.0,), (0.0,), (-1.0,), (float('inf'),), (float('-inf'),)]
# Specify schema
schema = ["value"]
# Create DataFrame
df = spark.createDataFrame(data, schema)
# Calculate inverse tangent
df = df.withColumn("atan_value", F.atan(F.col("value")))
# Show the result
df.show()``````
Output
``````+---------+-------------------+
|    value|         atan_value|
+---------+-------------------+
|      1.0| 0.7853981633974483|
|      0.0|                0.0|
|     -1.0|-0.7853981633974483|
| Infinity| 1.5707963267948966|
|-Infinity|-1.5707963267948966|
+---------+-------------------+
``````

The output will display the original values and the computed inverse tangent values. Note that the `atan` of infinity and negative infinity are π/2 and -π/2, respectively.

Potential applications and considerations:

The `atan` function is incredibly useful in various applications involving trigonometry, especially where one needs to compute angles from their tangent values. It’s also essential in coordinate transformations and dealing with circular motion in physics.

However, it’s important to handle exceptional cases, like the infinity values shown in the example, in your real-world data processing scripts.

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