A power series representation of sin(x), where x is an angle in radians, is as follows: sin(x) -x-+ n-0 n= 1 Write a MATLAB function m-file that iteratively approximates sin(x) using this formula until the absolute relative approximate error falls below a given tolerance: Your function must have two inputs (a scalar value for x, and a tolerance) and a single output (the computed approximation of sin(x)) . Iteratively compute the approximation of sin(x) o For each iteration, compute and compare the absolute relative approximate error to the tolerance, and stop if the error becomes less than the tolerance. . Just be fore your function ends, use fprintf to print out the number of iterations that were executed and the final absolute relative approximate error. Hint: Look at the examples in lecture6.pdf for computing a square root and for computing cos(r). Your code should combine elements of both For your demonstration: Set MATLAB's output format to longG . Show the function's output when computing sin(1/2) with a tolerance of 0.01 o Compute the absolute relative true error for vour result Show the function's output for another pair ofx and tolerance values A power series representation of sin(x), where x is an angle in radians, is as follows: sin(x) -x-+ n-0 n= 1 Write a MATLAB function m-file that iteratively approximates sin(x) using this formula until the absolute relative approximate error falls below a given tolerance: Your function must have two inputs (a scalar value for x, and a tolerance) and a single output (the computed approximation of sin(x)) . Iteratively compute the approximation of sin(x) o For each iteration, compute and compare the absolute relative approximate error to the tolerance, and stop if the error becomes less than the tolerance. . Just be fore your function ends, use fprintf to print out the number of iterations that were executed and the final absolute relative approximate error. Hint: Look at the examples in lecture6.pdf for computing a square root and for computing cos(r). Your code should combine elements of both For your demonstration: Set MATLAB's output format to longG . Show the function's output when computing sin(1/2) with a tolerance of 0.01 o Compute the absolute relative true error for vour result Show the function's output for another pair ofx and tolerance values