递归逼近正弦

Question

所以我正在尝试编写一个由两个递归函数组成的文件。其中之一计算通过泰勒级数逼近正弦所需的阶乘。第二个是另一个递归函数，它将正弦的值输出为浮点值，并且会一直到输入的项数为止。这是我想要得到的东西的数学表示

到目前为止，这是我的代码（由于我在实际正弦计算函数方面遇到困难，因此尚未完成）：

def main():
    ang = int(input("Enter the angle to approximate (in radians): "))
    trms = int(input("Enter the amount of terms to compute: "))
    sinApprox(ang,trms)
def calcFac(x):
    if x <= 0:
        return 1
    else:
        return x * calcFac(x-1)
def sinApprox(angle, terms):
    if calcFac(terms) <= 0:
        return (sinApprox(angle,terms)/calcFac(terms))
    elif terms % 2 == 0:
        return sinApprox(angle**)

请注意，这两个函数也必须是纯函数和递归函数。

Answer 1

这里有一种方法可以做到这一点。

def calcFac(x):
    if x == 1 or x == 0: return 1
    val = 1
    for i in range(2, x+1):
        val = val * i
    return val

def sinApprox(angle, terms):
    mult = 1
    if terms % 2 == 0: mult = -1

    power = 2*terms - 1
    val = angle ** power
    val = mult * val/calcFac(power)

    if terms == 1: return val
    else: return val + sinApprox(angle, terms - 1)

angle = int(input("Enter the angle to approximate (in radians): "))
terms = int(input("Enter the amount of terms to compute: "))
sinApprox(angle, terms)

递归逼近正弦

Approximating Sine recursively

python

recursion

trigonometry

series