Question about Taylor Series While loop.

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I'm completely stuck on this While Loop using Taylor Series.
x = input('Input the angle in radians: ');
Cos_Estimate = 0;
k = 0;
Errrr = 1
while Errrr > .000001
if mod(k,2)
Sign = 1;
else
Sign = -1;
end
k = k + 2;
Cos_Estimate = Cos_Estimate + (x^k/(factorial(k)*Sign));
Errrr = abs(Cos_Estimate - cos(x));
end
err = abs(Cos_Estimate - cos(x));
fprintf('The estimated cosine value based on the Taylor Series is: %0.6f \n',Cos_Estimate)
fprintf('The actual cosine value is : %0.6f \n',cos(x))
fprintf('The estimation error is: %0.6f \n',err)
fprintf('The number of terms required was: \n',term)
Now I am getting NaN for my variable. I'm stuck.

Accepted Answer

Azzi Abdelmalek
Azzi Abdelmalek on 6 Mar 2013
Edited: Azzi Abdelmalek on 6 Mar 2013
Try this
x = input('Input the angle in radians: ');
Cos_Estimate = 1;
Errrr=1
Sign = 1;
k = 0;
while Errrr > .000001 & k<60
Sign =-Sign;
k = k + 2;
Cos_Estimate = Cos_Estimate + (x^k/(factorial(k)*Sign))
Errrr = abs(Cos_Estimate - cos(x))
end
display(Cos_Estimate)

More Answers (2)

Babak
Babak on 6 Mar 2013
add this line to the beginning of your code:
Errrr =1;
  1 Comment
Derryn
Derryn on 6 Mar 2013
Added it, but now I get this as my output:
EDU>> Lab7_Prob3Script
Input the angle in radians: pi
The estimated cosine value based on the Taylor Series is: NaN
The actual cosine value is : -1.000000
The estimation error is: NaN
The number of terms required was:

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Azzi Abdelmalek
Azzi Abdelmalek on 6 Mar 2013
Edited: Azzi Abdelmalek on 6 Mar 2013
Your code never enter in the loop because Errrr is not defined
  5 Comments
Derryn
Derryn on 6 Mar 2013
Ah ok thanks. Does this look better?
x = input('Input the angle in radians: ');
Cos_Estimate = 0; k = 0;
count = 0;
Errrr = 1;
while Errrr > .000001
count = count + 1;
if mod(k,2)
Sign = 1;
else
Sign = -1;
end
k = k + 2;
Cos_Estimate = Cos_Estimate + (x^k/(factorial(k)*Sign));
Errrr = abs(Cos_Estimate - cos(x));
if k > 170
break
end
end
err = abs(Cos_Estimate - cos(x));
fprintf('The estimated cosine value based on the Taylor Series is: %0.6f \n',Cos_Estimate)
fprintf('The actual cosine value is : %0.6f \n',cos(x))
fprintf('The estimation error is: %0.6f \n',err)
fprintf('The number of terms required was: %0.0f \n',count)
I'm still getting the wrong value for Cos_Estimate

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