What is the problem with the following sin approximation?

I am being asked to take two inputs and spit out an approximation of sine and how many terms were being used in the approx. Here is the code with a while loop.

function [approx, terms] = approx_sine(x, threshold)
approx = x; % Initial approximation 
terms = 0; % Number of additional terms added to improve the approximation
% Write your code here using a while loop to improve the above approximation
real=sin(x);
n=1;
while threshold<abs((real-approx)/real)   
    if rem(n,2)==0
        X1=1;
        X2=0;
    else
        X2 = 1;
        X1=0;

      end

      approx=approx+ X1*(x^(2*n-1)/factorial(2*n-1))-X2*(x^(2*n-1)/factorial(2*n-1))

      n=n+1;
      terms=terms+1
  end
  end

the sine approx is equal to sin(x) = x−x3/3!+x5/5! −x7/7!+···

Answer 1

[Thorsten]

The formula is wrong. It's (-1)^(n)*x.^(2*n+1)/factorial(2*n+1) for the n'th term. Instead of your solution using X1 and X2, you can use (-1)^n:

function [approx, n] = approxsine(x, threshold)
approx = x; % Initial approximation 
n = 0; % Number of additional terms added to improve the approximation;
% Write your code here using a while loop to improve the above approximation
while threshold <= abs((sin(x)-approx)/sin(x))
   n = n + 1;
   approx = approx + (-1)^(n)*x.^(2*n+1)/factorial(2*n+1);
end
end

[William Schmidt]

I just figured this out as you answered. Here's the code that worked for me

function [approx, terms] = approx_sine(x, threshold)
approx = x; % Initial approximation 
terms = 0; % Number of additional terms added to improve the approximation

% Write your code here using a while loop to improve the above approximation
real=sin(x)
n=1;
while threshold<abs((real-approx)/real)

      if rem(n,2)==0
          X1=1;
          X2=0;
      else
          X2 = 1;
          X1=0;

      end
      n=n+1;
      approx=approx+ X1*(x^(2*n-1)/factorial(2*n-1))-X2*(x^(2*n-1)/factorial(2*n-1))

      terms=terms+1

end
end

[Image Analyst]

Maybe you could Accept and Vote for his answer anyway, since his answer was right and he took the time to help you. It will give him "Reputation points" towards more powers in this forum.