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

Syntax

import math
result = math.sin(x)

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

Return Value

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

Examples

1. Calculating the sine of an angle in radians:

   import math
   
   result = math.sin(math.pi / 2)  # Sine of 90 degrees (π/2 radians)
   print(result)  # Output: 1.0
   

2. Calculating the sine of other angles:

   result = math.sin(math.pi)  # Sine of 180 degrees (π radians)
   print(result)  # Output: 0.0
   
   result = math.sin(0)  # Sine of 0 degrees (0 radians)
   print(result)  # Output: 0.0
   
   result = math.sin(-math.pi / 2)  # Sine of -90 degrees (-π/2 radians)
   print(result)  # Output: -1.0
   

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

   angle_deg = 30
   result = math.sin(math.radians(angle_deg))  # Sine of 30 degrees
   print(result)  # Output: 0.49999999999999994 (approximately 1/2)
   

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

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

Summary

• The math.sin() function computes the sine 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.