how to use a while loop to perform an infinite series approximation

Question

Joe 2012-7-2

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评论： steven mcquade 2016-11-1

So I have to write a program using a while loop that uses the alternating series approximation for sin(x) using a while loop and compare it to the matlab sin(x) using an error function. so far I have:

clc
clear
x=input('Enter the value of x to compute sin(x): ');
error=1;
n=0;
while error >= 1*(10^-5);
     terms = ((-1)^n)*(((x^(n+1)))/factorial(n+1));
     SINx=sum(terms);
     n=n+1;
     error=abs((sin(x)-SINx)/sin(x))*100; 
  end

And my loop does nothing. Any ideas?

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steven mcquade 2016-11-1

you haven't told it to print an answer

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Answer 1

Tom 2012-7-2

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编辑：Tom 2012-7-2

在 MATLAB Online 中打开

Here's a shabby way of doing it...

 x=pi/2; %test: sin(pi/2)=1;
error=1;
n=1;
count=0;
while error >= 1*(10^-3);
  %x -x^3/3! +x^5/5! ...
  count=count+1;
  terms(count)=(-1)^(count+1)*(x^n)/factorial(n);
  SINx=sum(terms);
  n=n+2;
  error=abs((sin(x)-SINx)/sin(x))*100;
end
  disp(SINx)

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Joe 2012-7-2

that helped immensely thank you!

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Answer 2

Walter Roberson 2012-7-2

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You are only generating a single value in "terms", and the sum() is being applied to that single value. You are not accumulating the values from the terms with n=0, n=1, n=2, etc..

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Tom 2012-7-2

That is true; also I think the series is incorrect- sine is something like this:x -x^3/3! +x^5/5! ...

Joe 2012-7-2

yes I see the error in the series -- I have to fix where the N starts counting for it to be right -- but how do I accumulate the n terms? do I need the while loop to be embedded in a For loop or vice versa?

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