The function fi(r,8)cos(x 8) cos(x) can be transforme using the trigonometric formula d into another form, f2x,8) cos(d) _ cos()-:-2 sin (-_ ) sin Thus, fi and f2 have the same values, in exact arithmetic, for any given argument values x and . (a) Show that, analytically, fi (x,8)/8 or f2(x,8)/d are effective approximations of the func- tion-sin(x) for sufficiently small. (b) Derive 2(x,8 (c) Write a MATLAB script which will calculate gi(x,8-fi(x, )/+sin(x) and g2(x,8) f2(x, )/6 + sin(x ) for x-3 and -Le-11- d) Explain the difference in the results of the two calculations. The function fi(r,8)cos(x 8) cos(x) can be transforme using the trigonometric formula d into another form, f2x,8) cos(d) _ cos()-:-2 sin (-_ ) sin Thus, fi and f2 have the same values, in exact arithmetic, for any given argument values x and . (a) Show that, analytically, fi (x,8)/8 or f2(x,8)/d are effective approximations of the func- tion-sin(x) for sufficiently small. (b) Derive 2(x,8 (c) Write a MATLAB script which will calculate gi(x,8-fi(x, )/+sin(x) and g2(x,8) f2(x, )/6 + sin(x ) for x-3 and -Le-11- d) Explain the difference in the results of the two calculations