App: Math Module#

Section Title: Math

The math module provides most commonly used mathematical functions and constants.

  • First, you need to import the math module.

import math

You can access the list of constants and functions in the math module by using the dir(math) function.

  • You can execute help(math) for more details.

print(dir(math))

['__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh', 'cbrt', 'ceil', 'comb', 'copysign', 'cos', 'cosh', 'degrees', 'dist', 'e', 'erf', 'erfc', 'exp', 'exp2', 'expm1', 'fabs', 'factorial', 'floor', 'fmod', 'frexp', 'fsum', 'gamma', 'gcd', 'hypot', 'inf', 'isclose', 'isfinite', 'isinf', 'isnan', 'isqrt', 'lcm', 'ldexp', 'lgamma', 'log', 'log10', 'log1p', 'log2', 'modf', 'nan', 'nextafter', 'perm', 'pi', 'pow', 'prod', 'radians', 'remainder', 'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'tau', 'trunc', 'ulp']

Constants#

pi#

\(\pi\) (pi): math.pi

print(math.pi)

3.141592653589793

e#

\(e\) (Euler’s constant): math.e

print(math.e)

2.718281828459045

Functions#

radians()#

It is the conversion function from degress to radians. The syntax is math.radians()

# 180 degrees = 1 pi radians
print(math.radians(180))

3.141592653589793

# 270 degrees = 3 pi /2 radians
print(math.radians(270))

4.71238898038469

degrees()#

It is the conversion function from radians to degrees. The syntax is math.degrees()

# 180 degrees = 1 pi radians
print(math.degrees(math.pi))

180.0

# 270 degrees = 3 pi /2 radians
print(math.degrees(3*math.pi/2))

270.0

cos()#

It is the cosine function. The syntax is math.cos()

  • The input angle is in radians.

# cos(0)
print(math.cos(0))

1.0

# cos(pi/2), actual value is 0
print(math.cos(math.pi/2))

6.123233995736766e-17

# cos(pi)
print(math.cos(math.pi))

-1.0

# cos(3pi/2), actual value is 0
print(math.cos(3*math.pi/2))

-1.8369701987210297e-16

# cos(2pi)
print(math.cos(2*math.pi))

1.0

sin()#

It is the sine function. The syntax is math.sin()

  • The input angle is in radians.

# sin(0)
print(math.sin(0))

0.0

# sin(pi/2)
print(math.sin(math.pi/2))

1.0

# sin(pi), actual value is 0
print(math.sin(math.pi))

1.2246467991473532e-16

# sin(3pi/2)
print(math.sin(3*math.pi/2))

-1.0

# cos(2pi), actual value is 0
print(math.sin(2*math.pi))

-2.4492935982947064e-16

tan()#

It is the tangent function. The syntax is math.tan()

  • The input angle is in radians.

# tan(0)
print(math.tan(0))

0.0

# tan(pi), actual value is 0
print(math.tan(math.pi))

-1.2246467991473532e-16

acos()#

It is the arccosine function which is the inverse of the cosine function. The syntax is math.acos()

# acos(1) = 0 because cos(0) = 1
print(math.acos(1))

0.0

asin()#

It is the arcsine function which is the inverse of the sine function. The syntax is math.asin()

# asin(1) = pi/2 because sin(pi/2) = 1
print(math.asin(1))

1.5707963267948966

atan()#

It is the arctangent function which is the inverse of the tangent function. The syntax is math.atan()

# atan(0) = 0 because tan(0) = 0
print(math.atan(0))

0.0

cosh()#

It is the hyperbolic cosine function. The syntax is math.cosh()

\(\displaystyle cosh(x) = \frac{e^x+e^{-x}}{2}\)

print(math.cosh(0))

1.0

print(math.cosh(1))

1.5430806348152437

sinh()#

It is the hyperbolic sine function. The syntax is math.sinh()

\(\displaystyle sinh(x) = \frac{e^x-e^{-x}}{2}\)

print(math.sinh(0))

0.0

print(math.sinh(1))

1.1752011936438014

tanh()#

It is the hyperbolic tangent function. The syntax is math.tanh()

\(\displaystyle tanh(x) = \frac{e^x-e^{-x}}{e^x+e^{-x}}\)

print(math.tanh(0))

0.0

print(math.tanh(1))

0.7615941559557649

lcm()#

It is the least common multiple function. The syntax is math.lcm()

print(math.lcm(12, 20))

60

gcd()#

It is the greatest common divisor function. The syntax is math.gcd()

print(math.gcd(12,20))

4

log()#

It is the logarithm to the base of \(e\) function \(\log_e(x)=ln(x)\). The syntax is math.log()

print(math.log(math.e))

1.0

log10()#

It is the logarithm to the base of \(e\) function \(\log_{10}(x)=log(x)\). The syntax is math.log10()

print(math.log10(1000))

3.0

factorial()#

It is the factorial function. The syntax is math.factorial()

  • 5 factorial is denoted by \(5!\) in mathematics and it is equal to \(5! = 5\cdot4\cdot3\cdot2\cdot1\)

print(math.factorial(5))

120

sqrt()#

It is the square root function. The syntax is math.sqrt()

print(math.sqrt(36))

6.0

comb()#

It returns the number of combinations of choosing k items from n items without repetition and without considering the order.

  • It’s also equivalent to the number of subsets with k elements in a set containing n elements.

    • Example: for the set {a,b,c,d,e} the subsets with 2 elements are:

      • {a,b}, {a,c}, {a,d}, {a,e}, {b,c}, {b,d}, {b,e}, {c,d}, {c,e}, {d,e}

  • comb(n,k) is denoted by \(C(n,k)\) in mathematics and it is equal to \(\displaystyle C(n,k) = \frac{n!}{(n-k)!\cdot k!}\)

  • The syntax is math.comb(n, k)

print(math.comb(5,2))

10

perm()#

It returns the number of permutations of choosing k items from n items without repetition but considering the order.

  • Example: for the set {a,b,c,d,e} the permutations with 2 elements are:

    • ab, ac, ad, ae, bc, bd, be, cd, ce, de

    • ba, ca, da, ea, cb, db, eb, dc, ec, ed

  • perm(n,k) is denoted by \(P(n,k)\) in mathematics and it is equal to \(\displaystyle P(n,k) = \frac{n!}{(n-k)!}\)

  • The syntax is math.perm(n, k)

print(math.perm(5,2))

20

ceil()#

It is the the smallest integer greater than or equal to the input number. The syntax is math.ceil()

print(math.ceil(4.567))

5

print(math.ceil(9.2))

10

floor()#

It is the the largest integer less than or equal to the input number. The syntax is math.floor()

print(math.floor(4.567))

4

print(math.floor(9.2))

9