Error in Python script

Question

Good afternoon

Can someone explain to me why my code does not give the requested result and what I can do to obtain the requested solution?

Error appears as follows: total = round(sum,Ndec[k])Typeerror: 'list' Object cannot be Interpreted as an integer

Implement a function with three parameters, which, for a given angle in degrees (first parameter), a vector N (second parameter), with increasing values of the number of terms of the series to be used, computes and returns a vector with the value of the approximation of the cosine function obtained with each of the Ni Taylor series terms, for given angle.

The number of decimal places to use in the result for each number of terms is given by the vector NDec (third parameter) with the index i of the vector indicating the number of decimal places to be displayed for the number of terms defined in the index i vector N. The vector N should not be modified by the function.

import math
def taylor(ang,N,NDec):
ang_rad = math.radians(ang)
res = []
soma = 0
for i in range(len(N)): 
    for k in range(len(NDec)):
        for j in range(N[i]):
            aprox_cos = (-1)**j/(math.factorial(2*j)) * ang_rad**(2*j)
            soma = soma + aprox_cos
        total = round(soma,NDec[k])
    res.append(total)
return res

I used it on the console

ang = 180

N=[3, 4, 6, 10, 20]

NDec=[4, 6, 8, 10, 10]

The solution is:

[0.1239, -1.211353, -1.0018291, -1.0000000035, -1.0]

Note:

Thanks to those who can help!

Answer 1

As far as I can tell, there’s one parenthesis left on line 7 and there’s an extra bracket on line 9.

I believe that fixing this errors do not appear. I tested in an online python environment.

Answer 2

The problem is simple, you are passing the Angule in degrees and the function should receive the angle in radians.

I refactored the code a little bit because I didn’t understand that sum of your initialized out of the loops. I created 2 methods, a called Taylor, which generates the results for each quantity of elements and a compute_cos, which uses the series of Taylor to calculate for 1 element.

def taylor(angle, vector, decimals):
    """Calcula a aproximacao do cosseno usando o metodo de Taylor

    Parameteres
    ----------
    angle : int angulo em graus
    vector : list com a quantidade de iteracoes a serem usadas pra aproximar o resultado
    decimals : quantidade de casas decimais do resultado
    """
    results = []

    for (i, element) in enumerate(vector):        
        _sum = compute_cos(element, angle)

        dec = decimals[i]
        result = round(_sum, dec)        
        results.append(result)

    return results


def compute_cos(iterations, angle):
    """Calcula aproximadamente o coseno de um angulo usando series de Taylor

    Parameters
    ----------
    iterations: quantidade de iteracoes na serie
    angle : int angulo a ser calculado o coseno em graus
    """
    _sum = 0

    angle = math.radians(angle)
    for n in range(iterations):
        fact = math.factorial(2 * n)
        dividendo = (-1) ** n
        cos = (dividendo / fact) * (angle ** (2 * n))
        _sum += cos

    return _sum

Running these results, we get:

angle = 180
elements = [3, 4, 6, 10, 20] 
decimals = [4, 6, 8, 10, 10]
taylor(angle, elements, decimals)
>> [0.1239, -1.211353, -1.0018291, -1.0000000035, -1.0]

That matches the result you expect.