how to calculate sine and cosine in python without using math

Good time of day! Here's the thing:

There is a need to accurately calculate the sine and cosine, with the possibility of changing the accuracy(as decimal.getcontext().prec=...).

Math, of course, does not provide such a possibility.

I honestly don't know which way to go at all

Author: Михаил, 2017-12-02
Source

2 answers

The documentation for the decimal module contains examples of calculating sin, cos: 

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
 2
Author: jfs, 2018-04-07 08:09:41

The best thing I found was the Taylor series.

Here's the function, if you're interested:

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)
 1
Author: Михаил, 2017-12-03 14:33:11