Question

The cosine function can be evaluated by the following infinite series as (where the angle x is given in radians) cos x =1--+ + 2! 4! 6! Create a second function M-file mycos that takes the angle x (in radians), and returns cos(x) with an absolute iterative error less than 1.0e-18. Test your function to find cosine of ?/2 and 2? Display the Expansion order, and the actual error (absolute error, not the relative one) and iterative error using fprintf statement. The true or actual value can be calculated from MATLAB's built-in function cos (). Apply a proper header to your display. A typical example is:

Answer 1

function result = My_Cos(x)
    err = 10^(-18);
    total = 1;
    sign = -1;
    i = 2;
    while true
        val = (sign * x^i / factorial(i));
        if abs(val) < err
            break;
        end
        total = total + val;
        i = i + 2;
        sign = sign * -1;
    end
  
    result = total;
end

octave:2 cos (pi/2) ans6.1232e-17 octave:3> cos (2*pi) ans1