Question

someone please do this corrcetly using matlab and following all instructions

1. (30 Points) It is known that the sine function can be expressed as: x(2k+1) sin(x) = (-1) +(2k + 1)! k=0 Truncate the series to compute the first seven estimates (ie, for k = 0,1,2,3,4,5, and 6) for x = You must use a for loop. All calculations and printing the table described below should be done from within the loop. For each estimate, determine the magnitude of both the true error and magnitude of the approximate percent relative error. Arrange your results in a table (use fprintf - see workshop 5) that has column 1 as the '# of Terms' included in the estimate, the second column the 'Estimate', the third column the 'True Error' and the fourth column the Magnitude of the Approximate Percent Relative Error, 'MAPRE' Express everything, except the number of terms, in decimal format with 10 digits after the decimal point. The header should look exactly like this: # of terms Estimate True Error MAPRE

Answer 1

Please find the required MATLAB script as the following:

%======================================================================

clear all;
clc;

x = pi/5; % Given x value
k=0:6;    % Given number of terms
sinx_approx = 0; % Initialization of approximation variable
fprintf('# of terms\t Estimate\t\t True Error\t\t   MAPRE\n');
fprintf('----------\t------------\t------------\t------------\n');
for i = k
sinx_approx = sinx_approx + ((-1)^i * (x^(2*i+1))/factorial(2*i+1));
fprintf('\t%d\t\t%0.10f\t%0.10f\t%0.10f\n',i,sinx_approx,abs(sin(x)-sinx_approx),abs(sin(x)-sinx_approx)*100/sin(x));
end

%======================================================================

output:

# of terms Estimate True Error MAPRE -- - on WNHOIT 0.6283185307 0.5869768285 0.5877928810 0.5877852104 0.5877852524 0.5877852523 0.5877852523 0.0405332784 0.0008084238 0.0000076287 0.0000000419 0.0000000002 0.0000000000 0.0000000000 6.8959332116 0.1375372743 0.0012978682 0.0000071298 0.0000000256 0.0000000001 0.0000000000

Hope this helps!

***************** PLEASE THUMBS UP!!!!!!!!!!!!!!!!! *****************