import math

def calculate_trigonometric_function(x: float) -> float:

    """This function refers to Taylor's theorm.
    A remainder for cos or sin at x follows Cauchy's remainder.
    The function has 2 steps. Step1 gets a degree of
    Taylor polynomial function at x. Step 2 calculates sin and cos at x
    and returns two values
    """

    # Step1: get a degree of Taylor polynomial function at x
    degree = 0
    error = 5 * 1e-6
    while True:
        # Upper limit of Cauchy's remainder for sin or cos at x
        upper_limit = x**degree / math.factorial(degree)
        if upper_limit < error:
            break
        else:
            degree += 1

    # Step2: Calculate sin, cos at x
    sin = 0
    cos = 0
    for i in range(degree):
        sin += (-1)**i * x**((2 * i) + 1) / math.factorial(2 * i + 1)
        cos += (-1)**i * x**(2 * i) / math.factorial(2 * i)

    return sin + cos

nfact = {1:1, 2:2}
accuracy = 10

def fact(n):
    global nfact
    if n in nfact:
        return nfact[n]
    else:
        ans = n*fact(n-1)
        nfact[n] = ans
        return ans

def sin(n):
    ans = 0
    for i in range(1, accuracy, 2):
        ans += (n ** i) / fact(i) * (-1) ** (i // 2)
    return ans

def cos(n):
    ans = 1
    for i in range(2, accuracy, 2):
        ans += (n ** i) / fact(i) * (-1) ** (i//2)
    return ans


x = float(input('input number: '))
print('result: ', sin(x) + cos(x))

import math

def calSin(x):
    range = 0.1**10
    x = x * math.pi / 180
    sin = x
    i = 1
    while x > range :
        x = x**(2*i + 1) / math.factorial(2*i + 1)
        sin += (-1)**(2*i + 1) * x
        i += 1
    return sin

def calCos(x):
    range = 0.1**8
    x = x * math.pi / 180
    cos = 1
    i = 1
    while x > range :
        x = x**(2*i) / math.factorial(2*i)
        cos += ((-1)**i) * x
        i += 1
    return cos


q = int(input('육십분법의 각을 입력하세요(예: 0 ~ 360) : '))
print('\nsin{0} + cos{0} = {1}'.format(q, calSin(q)+calCos(q)))