Any kinds of programming language is acceptable, but Latex is better, thx

1 + 2 Exercise 2.3.1. (10 points) Let 1 2 = sin(r) cos(27) 4 One of the exact solutions of f(x) = 0 is p = 1.8954942670... (the other two are 0 and -1.8954942670.-). Let {Pn}n> be the sequence of approximation to this specific root p gen- erated by Newton's method. (a) Write a program of Newton's method to solve the equation f(x) = 0) with any initial input. List your codes. (b) Choose po = 0.57. Use your codes developed in (a) to calculate p.30 (c) Choose po = 57. Calculate P30 again. (a) What if you choose po 10x? Plot all the values of (Pn), in this case. Explain briefly what you observe