Finding an approximation for cos(x) using for loops

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Laura
Laura 2013-11-17
评论： Weeraphol Egsaphung 2017-9-23
Hi there,
I recently got help on creating a script to calculate the value of cos(x) using for loops. The question asks:
"Write a script which will calculate the value of cos(x) (ask the user for the value of x and n):
cos(x)=( from k=1 –> n )∑(-1) ̂(k-1)(x ̂(2(k-1))/(2(k-1))!)
" I had real problems getting the answer and so asked a tutor to help me with it. She managed to get the code working but I failed to understand how it actually works. (her explanation was not very clear)
So, I have sat staring at it for ages and it still doesn't make sense to me.
Here it is:
% Ask user for values x, n
x=input('Please enter a value for x: '); %cos angle
x_rad=x*pi/180;
n=input('Please enter a value for n: '); %nth term
%factorial
fact=1;
sum=0;
for k=1:n
initial=-1;
for a=0:(k-1)
initial=(-1)*initial;
end
numerator=1;
for b=1:2*(k-1)
numerator=numerator*x_rad;
end
for t=1:2*(k-1)
fact=fact*t;
end
total=(initial*numerator)/fact;
sum=sum+total;
end
fprintf('cos(%d)=%6.6f \n',x,sum);
Can anyone explain how this code is working in the for loop? I am so confused.
Also, any advice on a simpler way to do this?
Thanks so much, Laura
  2 个评论
Laura
Laura 2013-11-17
All of them. I don't understand why we need nested for loops in the first place and why the end values for each one is different. (e.g. for b=1:2*(k-1))

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Umair Nadeem
Umair Nadeem 2013-11-17
编辑：Umair Nadeem 2013-11-17
The code has been developed using a more complex approach. You can simply implement the equation you gave above. Here is how to do it.
% Ask user for values x, n
x=input('Please enter a value for x: '); %cos angle
x_rad=x*pi/180;
n=input('Please enter a value for n: '); %nth term
% Initialize resultant variable
sum=0;
for k=1:n
initial = (-1)^(k-1);
numerator = x_rad^(2*(k-1));
denominator = factorial(2*(k-1));
total=(initial*numerator)/denominator;
sum=sum+total;
end
fprintf('cos(%d)=%6.6f \n',x,sum);
It will give the same result. You dont have to use nested for loops to calculate the values of ^ (to the power), you can do it right away.
Hope it helps
  1 个评论
Weeraphol Egsaphung
Weeraphol Egsaphung 2017-9-23
Hi, I wonder the value of >> fprintf('cos(%d)=%6.6f \n',x,sum); if I want it sin How could I use the code

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