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The math library is built-in, so you don’t need to install anything to use it. You can import it simply by using import math.
The math library provides several basic mathematical functions, similar to what you might find on a calculator.
import math
# Absolute value
abs_val = math.fabs(-10) # Output: 10.0
# Factorial
factorial_val = math.factorial(5) # Output: 120
These functions are useful for growth calculations, interest calculations, and scientific computations.
math.exp(x)): Returns e raised to the power of x.math.log(x): Natural logarithm (base e).math.log(x, base): Logarithm of x to a specified base.math.log10(x): Logarithm of x to base 10.math.log2(x): Logarithm of x to base 2. exp_val = math.exp(2) # e^2
log_val = math.log(10) # ln(10)
log10_val = math.log10(100) # log_10(100)
These functions are essential in algebra for handling exponents and square roots.
math.pow(x, y)): Returns x raised to the power of y.math.sqrt(x)): Returns the square root of x.x ** (1/3). power_val = math.pow(3, 4) # 3^4
sqrt_val = math.sqrt(16) # √16
cube_root = 27 ** (1/3) # ³√27
The library includes all basic trigonometric functions, which are helpful in geometry, physics, and engineering.
math.sin(x): Sine of x (x is in radians).math.cos(x): Cosine of x.math.tan(x): Tangent of x.math.asin(x): Inverse sine.math.acos(x): Inverse cosine.math.atan(x): Inverse tangent.math.radians(degrees): Converts degrees to radians.math.degrees(radians): Converts radians to degrees. angle_rad = math.radians(90) # Convert 90 degrees to radians
sin_val = math.sin(angle_rad) # Sine of 90 degrees
The library also offers functions for converting between radians and degrees, which is essential for working with angles in various units.
math.degrees(x): Converts radians to degrees.math.radians(x): Converts degrees to radians. degrees = math.degrees(math.pi) # Output: 180
radians = math.radians(180) # Output: π (approx 3.14159)
Imagine you’re standing a certain distance away from a building and you want to determine its height. If you know the angle of elevation (the angle between the ground and your line of sight to the top of the building) and the distance from where you’re standing to the building (the adjacent side of the right triangle), you can use the sine function to calculate the height of the building (the opposite side).
For a right triangle:
sin(theta) = opposite side/hypotenuse
Where:
However, in this case, since we have the angle of elevation and the distance (adjacent side), we can use the formula:
tan(theta) = opposite / adjacent
Python Code for Using Tangent and Sine to Calculate the Height
import math
# Given values
angle_degrees = 30 # Angle of elevation in degrees
distance_adjacent = 50 # Adjacent side (distance from the base in meters)
hypotenuse = 57.74 # Hypotenuse (line of sight in meters)
# Convert angle to radians
angle_radians = math.radians(angle_degrees)
# Calculate the height using tangent
height_tangent = distance_adjacent * math.tan(angle_radians)
# Calculate the height using sine
height_sine = hypotenuse * math.sin(angle_radians)
# Print results
print(f"Using Tangent: The height of the building is {height_tangent:.2f} meters.")
print(f"Using Sine: The height of the building is {height_sine:.2f} meters.")
math.radians(angle_degrees): Converts the angle from degrees to radians, as trigonometric functions in Python use radians.
Tangent Formula: The height is calculated using the tangent formula:
height = adjacent * tan(theta)
height = hypotenuse * sin(theta)
Using Tangent: The height of the building is 28.87 meters.
Using Sine: The height of the building is 28.87 meters.
This code calculates the height using both the tangent and sine functions, and you can see that both methods give the same result when the angle is (30^\circ), and the given values are used correctly.
The math library provides access to several useful mathematical constants:
math.pi): Ratio of a circle’s circumference to its diameter (~3.14159).math.e): Base of the natural logarithm (~2.71828).math.tau): Ratio of a circle’s circumference to its radius (~6.28318). print(math.pi) # 3.14159
print(math.e) # 2.71828
print(math.tau) # 6.28318
Rounding functions are useful for rounding numbers to the nearest integer or truncating decimal values.
math.ceil(x)): Rounds x up to the nearest integer.math.floor(x)): Rounds x down to the nearest integer.math.trunc(x)): Truncates x to the integer part only. ceil_val = math.ceil(4.3) # Output: 5
floor_val = math.floor(4.7) # Output: 4
trunc_val = math.trunc(4.9) # Output: 4
math.gcd(x, y)): Finds the greatest common divisor of x and y.math.lcm(x, y)): Finds the least common multiple of x and y (available in Python 3.9+). gcd_val = math.gcd(8, 12) # Output: 4
lcm_val = math.lcm(4, 6) # Output: 12 (Python 3.9+)
| Function Type | Examples |
|---|---|
| Basic Functions | math.fabs, math.factorial |
| Exponential and Logarithmic | math.exp, math.log, math.log10 |
| Power and Roots | math.pow, math.sqrt |
| Trigonometric Functions | math.sin, math.cos, math.tan |
| Hyperbolic Functions | math.sinh, math.cosh, math.tanh |
| Angular Conversion | math.degrees, math.radians |
| Special Constants | math.pi, math.e, math.tau |
| Rounding and Precision | math.ceil, math.floor, math.trunc |
| GCD and LCM | math.gcd, math.lcm |
| Combinatorics | math.perm, math.comb |
The math library is a comprehensive toolset for performing a wide range of mathematical calculations, making Python versatile for both basic and advanced math applications. Let me know if you’d like further details or examples on any specific function!
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[1] Python Software Foundation, “Math — Mathematical Functions — Python 3.13 Documentation,” docs.python.org, 2024. https://docs.python.org/3/library/math.html
For more details, see Appendix A.