Implement a function using loops that uses the taylor series to approximate the value of the cosine function.

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cosx=∑n=0∞(−1)n(2n)!x2n=1−x22!+x44!−⋯
as n increases, our summation term becomes a more and more accurate approximation of cos(x), and an infinite number of terms would precisely equal cos(x). (Note: x is in radians.)

Obviously we can't add up an infinite number of terms in the real world, so instead if we implement this as a function in C++, we must specify how many terms of the summation we want to use. (In other words, the upper bound of the sum stops being infinite.)
Thus, your function will take two parameters: the value x (in radians) as the number of terms to use when approximating the solution. Thus, if my test code calls approxCosine(1.5, 3), you should return the sum of the first 3 terms of the cosine approximation:

approxCosine(1.5,3)=∑n=02(−1)n(2n)!x2n=1−x22!+x44!

What I have tried:

i do not know from where to start

Posted 21-Jun-17 17:49pm

Member 13272542

Updated 21-Jun-17 21:52pm

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Patrice T · Answer 1 · 2017-06-21T18:05:00

Seriously ? your main effort was to paste the statement.

Quote:
i do not know from where to start

The answer is in the question. The first thing to do is to read the statement.

Quote:
Thus, your function will take two parameters: the value x (in radians) and the number of terms to use when approximating the solution. Thus, if my test code calls approxCosine(1.5, 3), you should return the sum of the first 3 terms of the cosine approximation:

We do not do your HomeWork.
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That's not the same thing as "have a quick google and give up if I can't find exactly the right code".

CPallini · Answer 2 · 2017-06-21T21:52:00

Quote:
i do not know from where to start

The general term of the cosine taylor expansion is (-1)ⁿx²ⁿ/(2n!).
The first step could be writing such as a C++ expression. The prerequisite is writing the factorial function, that is not provided.

So, supposing you've written your own factorial function (say fact), then you might write

C++

term[n] = pow(x, 2.0 * n) / fact(2 * n);
if ((n % 2) == 1) term[n] = -term[n]; // for n odd, the term is negative

Implement a function using loops that uses the taylor series to approximate the value of the cosine function.

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