如何在不使用数学的情况下在python中计算正弦和余弦

decimal 模块的文档包含计算 sin、cos 的示例：

def sin(x):
    """Return the sine of x as measured in radians.

    The Taylor series approximation works best for a small value of x.
    For larger values, first compute x = x % (2 * pi).

    >>> print(sin(Decimal('0.5')))
    0.4794255386042030002732879352
    >>> print(sin(0.5))
    0.479425538604
    >>> print(sin(0.5+0j))
    (0.479425538604+0j)

    """
    getcontext().prec += 2
    i, lasts, s, fact, num, sign = 1, 0, x, 1, x, 1
    while s != lasts:
        lasts = s
        i += 2
        fact *= i * (i-1)
        num *= x * x
        sign *= -1
        s += num / fact * sign
    getcontext().prec -= 2
    return +s

我发现最好的东西是泰勒系列。

如果您有兴趣，这是功能：

def q(x):
    Decimal(x)
def sin(x):
    tmp=getcontext().prec
    getcontext().prec=tmp+50
    x=q(x)
    n=x
    r = 0;
    i = 1;
    while ((-n,n)[n>0] > q("1E-"+str(getcontext().prec))):
        r += n;
        n *= q(-1) * x * x / ((2 * i) * (2 * i + 1));
        i+=1
    getcontext().prec=tmp
    return q(r)