#Number Basics

import math

print(math.ceil(4.3))

5

print(math.floor(4.8))

4

print(math.floor(-4.2))

-5

print(math.fabs(-3.7))

3.7

print(math.fabs(3.7))

3.7

print(math.trunc(3.9)) 

3

print(math.trunc(-3.9))

-3

print(math.copysign(10, -1))

-10.0

print(math.copysign(0, -5))

-0.0

print(math.fmod(20, 3))

2.0

print(math.fmod(7.5, 2.0)) 

1.5

print(math.isclose(0.1 + 0.2, 0.3)) 

True

print(math.isclose(0.1 + 0.2, 0.3001))  # False

False

print(math.remainder(7, 3)) 

1.0

print(math.remainder(-7, 3))  # -1.0

-1.0

print(math.modf(2.75))  # (0.75, 2.0)

(0.75, 2.0)

print(math.isfinite(10))  # True

True

print(math.isfinite(math.inf))

False

print(math.isnan(math.nan))

True

print(math.isnan(5.0)) 

False

print(math.isinf(math.inf)) 

True

print(math.isinf(100))

False

print(math.frexp(8)) 

(0.5, 4)

print(math.frexp(10.5)) 

(0.65625, 4)

print(math.ldexp(0.5, 3)) 

4.0

print(math.ldexp(0.65625, 4))

10.5

print(math.copysign(0.0, -0.0)) 

-0.0

print(math.modf(0))

(0.0, 0.0)

#Power, Roots, and Logarithms 

print(math.pow(2, 3))  

8.0

print(math.pow(4.5, 2))

20.25

print(math.sqrt(16)) 

4.0

print(math.sqrt(2.25))

1.5

print(math.isqrt(10))

3

print(math.isqrt(25))

5

print(math.exp(1))

2.718281828459045

print(math.exp(-1)) 

0.36787944117144233

print(math.expm1(0.01))

0.010050167084168058

print(math.log(10))

2.302585092994046

print(math.log10(1000)) 

3.0

print(math.log2(32))

5.0

print(math.log1p(1e-5)) 

9.99995000033333e-06

print(math.log(25, 5))

2.0

print(math.pow(9, 0.5)) 

3.0

print(math.sqrt(0))

0.0

print(math.isqrt(0))

0

print(math.log1p(0))

0.0

print(math.exp(0))

1.0

print(math.expm1(0))

0.0

print(math.log(1))

0.0

print(math.log2(1))

0.0

print(math.log10(1))

0.0

print(math.pow(2, -2)) 

0.25

print(math.log(math.e)) 

1.0

print(round(math.exp(5), 2)) 

148.41

print(math.pow(10, 6)) 

1000000.0

print(math.sqrt(1000000)) 

1000.0

try:
    print(math.log(-1))  # Error
except ValueError:
    print("Math domain error")

Math domain error

try:
    print(math.sqrt(-9))  # Error
except ValueError:
    print("Math domain error")

Math domain error

#Trigonometry Functions 

print(math.sin(0))

0.0

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

1.0

print(math.sin(math.pi)) 

1.2246467991473532e-16

print(math.cos(0))

1.0

print(math.cos(math.pi))

-1.0

print(math.tan(0))

0.0

print(math.tan(math.pi / 4))

0.9999999999999999

try:
    print(math.tan(math.pi / 2))  # very large
except:
    print("Undefined")

1.633123935319537e+16

print(math.asin(1)) 

1.5707963267948966

print(math.asin(0))

0.0

print(math.acos(1))

0.0

print(math.acos(0))  

1.5707963267948966

print(math.atan(1))

0.7853981633974483

print(math.atan(0))

0.0

print(math.atan2(1, 1)) 

0.7853981633974483

print(math.atan2(-1, -1)) 

-2.356194490192345

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

-1.0

print(math.cos(-math.pi))

-1.0

print(math.tan(-math.pi / 4))

-0.9999999999999999

try:
    print(math.asin(2))
except ValueError:
    print("Invalid domain")

Invalid domain

try:
    print(math.acos(-2))
except ValueError:
    print("Invalid domain")

Invalid domain

print(math.atan(-1))

-0.7853981633974483

print(math.sin(math.radians(30)))

0.49999999999999994

print(math.cos(math.radians(60))) 

0.5000000000000001

print(math.tan(math.radians(45)))

0.9999999999999999

x = math.pi / 6
print(math.asin(math.sin(x))) 

0.5235987755982988

print(math.acos(math.cos(x))) 

0.5235987755982987

print(math.atan(math.tan(x)))

0.5235987755982988

print(math.atan2(0, 0))  

0.0

print(math.atan2(1, -1))

2.356194490192345

#Angle Conversions & Constants 

print(math.degrees(math.pi))  

180.0

print(math.degrees(math.pi / 2)) 

90.0

print(math.degrees(2 * math.pi))

360.0

print(math.radians(180))

3.141592653589793

print(math.radians(90)) 

1.5707963267948966

print(math.radians(360))

6.283185307179586

print(math.hypot(3, 4)) 

5.0

print(math.hypot(0, 5))

5.0

print(math.hypot(-3, 4))

5.0

print(math.isclose(1.0001, 1.0002, rel_tol=1e-3)) 

True

print(math.pi)  

3.141592653589793

print(math.e)

2.718281828459045

print(math.tau) 

6.283185307179586

print(math.inf) 

inf

print(math.nan)

nan

print(math.isfinite(math.nan)) 

False

print(math.isinf(-math.inf)) 

True

print(math.isnan(0))

False

r = 3
print(math.pi * r**2)

28.274333882308138

print(math.tau * r) 

18.84955592153876

deg = 60
rad = math.radians(deg)
print(math.degrees(rad))

59.99999999999999

print(math.hypot(3, 4, 12))

13.0

print(math.atan2(1, 0))

1.5707963267948966

print(math.atan2(-1, 0))

-1.5707963267948966

print(math.tau / 2)

3.141592653589793

r = 5
print((math.pi * r ** 2) / 2)

39.269908169872416

print(math.isclose(1.001, 1.002, abs_tol=0.01)) 

True

print(math.e ** 2)

7.3890560989306495

print(math.log(math.e))

1.0

print(math.radians(0))

0.0

print(math.factorial(5)) 

120

print(math.factorial(0))

1

print(math.factorial(1))

1

print(math.comb(5, 2))

10

print(math.comb(4, 4)) 

1

print(math.comb(6, 0))

1

print(math.perm(5, 2)) 

20

print(math.perm(4, 4)) 

24

print(math.perm(7, 0)) 

1

print(math.gamma(5))

24.0

print(math.gamma(2.5))

1.3293403881791372

print(math.lgamma(5))

3.178053830347945

print(math.lgamma(1)) 

0.0

print(math.gamma(0.5))

1.7724538509055159

print(math.lgamma(0.5))

0.5723649429247004

print(math.factorial(10)) 

3628800

print(math.comb(10, 3))

120

print(math.perm(10, 3))

720

print(math.gamma(1)) 

1.0

print(math.gamma(2)) 

1.0

print(math.gamma(3))

2.0

print(math.gamma(4))

6.0

print(math.lgamma(2)) 

0.0

print(math.comb(20, 10))  

184756

print(math.perm(8, 5))

6720

print(round(math.gamma(4.5), 2)) 

11.63

print(round(math.lgamma(4.5), 2)) 

2.45

try:
    print(math.factorial(-5))
except ValueError:
    print("Negative factorial error")

Negative factorial error

try:
    print(math.comb(4, 5))
except ValueError:
    print("k > n error")

0

try:
    print(math.perm(4, 5))
except ValueError:
    print("k > n error")

0

#Advanced, Nested, and Composed Usage 

x = math.pi / 4
print(round(math.sin(x)**2 + math.cos(x)**2, 5))  # 1.0

1.0

a, b, c = 1, -3, 2
root1 = (-b + math.sqrt(b**2 - 4*a*c)) / (2*a)
print(root1)

2.0

v = (3, 4)
print(math.hypot(*v))  # 5.0

5.0

deg = 75
print(math.degrees(math.radians(deg)))  # 75.0

75.0

dx = 4
dy = 3
print(math.degrees(math.atan2(dy, dx)))  # 36.87...

36.86989764584402

x = 1.5
print(1 / (1 + math.exp(-x)))

0.8175744761936437

a, b = 100, 10
print(math.log(a) / math.log(b))  # log base 10

2.0

a, b, c = 5, 5, 6
s = (a + b + c) / 2
area = math.sqrt(s * (s - a) * (s - b) * (s - c))
print(area)

12.0

A0, k, t = 100, 0.1, 5
print(A0 * math.exp(-k * t))

60.653065971263345

P, r, n, t = 1000, 0.05, 12, 10
print(P * math.pow(1 + r/n, n*t))

1647.00949769028

print(math.sin(math.radians(30)))  # 0.5

0.49999999999999994

print(math.atan2(-3, -3))

-2.356194490192345

print(math.hypot(3, 4, 12)) 

13.0

angle = -3
print((angle + 2 * math.pi) % (2 * math.pi))

3.2831853071795862

d = 30
r = math.radians(d)
s = math.sin(r)
print(s)

0.49999999999999994

x = math.pi / 3
print((math.sin(x) + math.cos(x)) / 2)

0.6830127018922194

decimal, whole = math.modf(3.75)
print(whole, decimal)

3.0 0.75

x = 1e-10
print(math.log1p(x))

9.999999999500001e-11

print(math.expm1(x))

1.00000000005e-10

a, b = 4, 6
print(2 * a * b / (a + b))

4.8

a, b = 4, 9
print(math.sqrt(a * b))

6.0

r = 10
theta = math.radians(60)
print(r * theta)

10.471975511965976

print(0.5 * r**2 * theta)

52.35987755982988

print(math.sin(math.tau))  # ~0
print(math.cos(math.tau))  # ~1

-2.4492935982947064e-16
1.0

a, b = 10, 0
try:
    result = a / b
    print(math.isfinite(result))
except ZeroDivisionError:
    print("Divide by zero!")

Divide by zero!

x, min_x, max_x = 7, 5, 15
print((x - min_x) / (max_x - min_x))

0.2

print(((x - min_x) / (max_x - min_x)) * 100)

20.0

r, theta = 5, math.radians(60)
x = r * math.cos(theta)
y = r * math.sin(theta)
print(x, y)

2.5000000000000004 4.330127018922193

r = math.hypot(x, y)
theta = math.degrees(math.atan2(y, x))
print(r, theta)

5.0 59.99999999999999

a, b, angle = 3, 4, math.radians(90)
c = math.sqrt(a**2 + b**2 - 2*a*b*math.cos(angle))
print(c)  # Should be 5

5.0