泰勒級數求 sinx

def fact(n):
    if n <= 1:
        return 1
    else:
        return n * fact(n - 1)

def taylor_sin(x, m):
    value = 0
    eps = 1e-18
    for i in range(1, m + 1):
        value += ((-1) ** (i - 1)) * ((x ** (2*i-1)) / fact(2*i-1))
        if i == 1:
            last = value
            #print(i, last, value, abs(value-last))
        else:
            #print("i=",i, "last=",last, "value=", value, "a-b=",abs(value-last))
            if abs(value-last) < eps:
                return value
            else:
                last = value
def taylor_cos(x, m):
    a = 1
    count = 1
    for k in range(1, m):
        if count%2 != 0:
            a -= (x**(2*k)) / fact(2*k)
        else:
            a += (x**(2*k)) / fact(2*k)
        count += 1
    return a
    
def sin(x):
    return taylor_sin(x, 300)
    
def cos(x):
    return taylor_cos(x, 100)
x = 1
#print("sin(",x ,")=", sin(x, 100))
print("sin(%d)= %.12f"%(x, sin(x) ))
#print("cos(%d)= %.12f"%(x, cos(x) ))