Python Function to Calculate and Convert Radians to Degrees

Introduction

Radians and degrees are two common units for measuring angles. While degrees are more intuitive for everyday use, radians are the standard unit in many scientific and mathematical contexts, particularly in calculus and physics.

The conversion between radians and degrees is straightforward but important to understand when working with trigonometric functions in Python or other programming languages.

Formula

The conversion from radians to degrees can be calculated using the following formula:

Where π (pi) is approximately 3.141592653589793. This formula works because a full circle is 360 degrees or 2π radians, so the conversion factor is 180/π.

Python Function

Here's a simple Python function to convert radians to degrees:

import math

def radians_to_degrees(radians):
    """Convert radians to degrees."""
    degrees = radians * (180 / math.pi)
    return degrees

The function uses Python's built-in math.pi constant for the value of π. The input is in radians, and the output is in degrees.

Examples

Let's look at a few examples of how to use the function:

Example 1: Converting π/2 radians to degrees

import math

result = radians_to_degrees(math.pi / 2)
print(result)  # Output: 90.0

π/2 radians is equivalent to 90 degrees, which is a right angle.

Example 2: Converting π radians to degrees

import math

result = radians_to_degrees(math.pi)
print(result)  # Output: 180.0

π radians is equivalent to 180 degrees, which is a straight angle.

Example 3: Converting 1 radian to degrees

result = radians_to_degrees(1)
print(result)  # Output: 57.29577951308232

1 radian is approximately 57.2958 degrees.

Applications

Converting radians to degrees is useful in various fields:

• Trigonometry: Many trigonometric functions in Python use radians, so converting to degrees can make results more intuitive.
• Physics: Many physical laws and equations use radians, so conversions are necessary for practical applications.
• Computer Graphics: Rotations and transformations often require angle conversions between radians and degrees.
• Engineering: Design and analysis often involve angle measurements that need to be converted for different calculations.