How do I approach questions such as the following?

Question

1.00/5 (2 votes)

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Write a function (called sin_approx) that takes two inputs, namely the value x for the series above and an accuracy acc. This function must compute and return sin(𝑥) using the series above, within the given accuracy.
For example, if 𝑥 = 𝜋/5 and acc=1e-3 this function should return 0.5869768284775588

What I have tried:

Python

import math

def sin_approx(x, acc):
    approx = 0
    term1 = x
    n = 1
    while abs(term1)>= acc:
        
        approx += term1
        n += 2
        term1 = ((-1)*(n//2))*(x**n)/math.factorial(n)
                 
    return approx

Posted 16-Apr-23 19:47pm

Angela@231

Updated 16-Apr-23 21:11pm

CPallini

v2

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CPallini · Answer 1 · 2023-04-16T20:44:00

Solution 2

You should go on a step further, with the approximation. Try

Python

import math
  
def sin_approx(x, acc):
    approx = 0
    term1 = x
    n = 1
    while True:
        approx += term1
        if term1 < acc:
            break
        n += 2
        term1 = ((-1)*(n//2))*(x**n)/math.factorial(n)

    return approx

Posted 16-Apr-23 20:44pm

CPallini

Comments

OriginalGriff 17-Apr-23 2:53am

Fixing his homework for him ... it's far more fun if he works that out for himself ... :laugh:

OriginalGriff · Answer 2 · 2023-04-16T20:07:00

Without seeing the series that your homework refers to, we can't be specific - but the best guess is that the formula you are using is slightly wrong.

Manually work out what each term in the series formula should be for the first 5 or 6 terms, and compare them against the values your code calculates. When they differ, you can start looking more closely at why.