The math.cos() function in Python is used to calculate the cosine of a given angle. Similar to the sine function, the angle must be provided in radians, and the function returns the cosine value as a float. The cosine function is a fundamental mathematical function in trigonometry, which finds applications in physics, engineering, and computer graphics.

Syntax

import math
result = math.cos(x)

• x: The angle in radians for which you want to calculate the cosine.

Return Value

• Returns the cosine of the angle x as a float. The result will be in the range $[-1, 1]$.

Examples

1. Calculating the cosine of an angle in radians:

   import math
   
   result = math.cos(math.pi)  # Cosine of 180 degrees (π radians)
   print(result)  # Output: -1.0
   

2. Calculating the cosine of other angles:

   result = math.cos(0)  # Cosine of 0 degrees (0 radians)
   print(result)  # Output: 1.0
   
   result = math.cos(math.pi / 2)  # Cosine of 90 degrees (π/2 radians)
   print(result)  # Output: 0.0
   
   result = math.cos(-math.pi / 2)  # Cosine of -90 degrees (-π/2 radians)
   print(result)  # Output: 0.0
   

3. Using math.cos() with angles in degrees: If you have an angle in degrees, you can convert it to radians using math.radians() before calculating the cosine:

   angle_deg = 60
   result = math.cos(math.radians(angle_deg))  # Cosine of 60 degrees
   print(result)  # Output: 0.5000000000000001 (approximately 1/2)
   

4. Using math.cos() in expressions: You can use math.cos() in more complex calculations:

   angle_rad = math.pi / 4  # 45 degrees
   result = math.cos(angle_rad) ** 2 + math.sin(angle_rad) ** 2
   print(result)  # Output: 1.0 (because cos(45)^2 + sin(45)^2 = 1)
   

Summary

• The math.cos() function computes the cosine of an angle in radians.
• The result is always a float and lies within the range of $[-1, 1]$.
• This function is essential in trigonometry and is widely used in various applications, including physics, engineering, and computer graphics, where waveforms and periodic functions are involved.