MATLAB: I need help creating a loop.

doit4meloopsinx

Our teacher asked us to create a loop that calculates sin(x) to nth number of terms.

our professor obviously doesnt know how to use matlab because he has not helped us at all.

can someone help with this? i want to learn and comprehend what is going on?

-sin(x) = x-(x^3/3!)+(x^5/5!)-(x^7/7!
-The calculation should stop when the magnitude of the last terms is less than .0000006, it should work for positive and negative values
-The function should return the estimate and number of terms required to get this accuracy

After___terms sin(__) is approximated to be_____.

Best Answer

Here's a hint

x = 1.234; % Whatever...
theSum = 0;
for term = 1 : 10000
  thisTerm = ...... % you do it.  Involves x and term.
  theSum = theSum + thisTerm;  % Accumulate
  if abs(thisTerm) < .0000006
    break;
  end
end
fprintf('The final sum = %f', theSum);

Related Solutions

MATLAB: How to use a while loop to perform an infinite series approximation

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)

MATLAB: How to approximate cosine with taylor series expansion and while loops

Taylor series for cos(x) is

1 - x^2/2! + x^4/4! - x^6/6! + ...

So, you are missing that first term of 1 and your x exponent value of "2*count" is not matching your factorial value of "count" when compared to this series (they should be the same value ... e.g. the "2n" from the formula you post above).

To correct this, make the first terms value 1, e.g. put this line before the while loop

terms(1) = 1;

Then bump up the terms indexing so you don't overwrite that first value, e.g.,

terms(count+1) = ...

Then correct that factorial argument so it matches the exponent, e.g.,

.../factorial(2*count)

Since you are apparently running this in a script, you need to clear terms from your workspace before running this script. Otherwise you will be left with your old terms result when you start this script. Either put all of this code inside of a function so that you always start with a clean workspace (my preferred approach), or you can just make sure terms is cleared first. E.g. put this line at the top of your script:

clear terms

There is one other problem in your code which I will let you find ...

Best Answer

Related Solutions

MATLAB: How to use a while loop to perform an infinite series approximation

MATLAB: How to approximate cosine with taylor series expansion and while loops

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