The math.tan() function in Python is used to calculate the tangent of a given angle. Like the sine and cosine functions, the angle must be provided in radians, and the function returns the tangent value as a float. The tangent function is a fundamental mathematical function in trigonometry and has applications in various fields such as physics, engineering, and computer graphics.

Syntax

import math
result = math.tan(x)

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

Return Value

• Returns the tangent of the angle x as a float. The tangent can take any real number value, ranging from $-\infty$ to $+\infty$.

Examples

1. Calculating the tangent of an angle in radians:

   import math
   
   result = math.tan(math.pi / 4)  # Tangent of 45 degrees (π/4 radians)
   print(result)  # Output: 1.0
   

2. Calculating the tangent of other angles:

   result = math.tan(0)  # Tangent of 0 degrees (0 radians)
   print(result)  # Output: 0.0
   
   result = math.tan(math.pi / 2)  # Tangent of 90 degrees (π/2 radians)
   print(result)  # Output: Infinity (since tan(90) is undefined)
   
   result = math.tan(-math.pi / 2)  # Tangent of -90 degrees (-π/2 radians)
   print(result)  # Output: -Infinity (since tan(-90) is undefined)
   

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

   angle_deg = 30
   result = math.tan(math.radians(angle_deg))  # Tangent of 30 degrees
   print(result)  # Output: 0.5773502691896257 (approximately)
   

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

   angle_rad = math.pi / 3  # 60 degrees
   result = math.tan(angle_rad) + 1
   print(result)  # Output: 2.7320508075688776 (approximately)
   

Summary

• The math.tan() function computes the tangent of an angle in radians.
• The result is always a float and can vary widely, as the tangent function can approach infinity for certain angles (specifically, odd multiples of $\frac{\pi}{2}$).
• This function is essential in trigonometry and is widely used in various applications, including physics, engineering, and computer graphics, particularly when dealing with slopes, angles, and periodic phenomena.