3. The sine function can be approximated by a polynomial according to the following formula:

(see image above for formula)

The error in the approximation S(x;n) decreases as n increases. The purpose of this exercise is to visualize the quality of various approximation s of S(x;n) as n increases. Complete the following.

(a) Write a function S(x,n) that computes S(x;n).

(b) Plot sin x on [0,4pi] together with the approximation S(x;1), S(x;2), S(x;3), S(x;6), and S(x;12).

(Solve the problem in Jupyter)

3. The sine function can be approximated by a polynomial according to the following formula: 7n sin 193(x; n)- (-1)/ (2j + 1)! The error in the approximation S(x; n) decreases as n increases. The purpose of this exercise is to visual the quality of various approximations of S(x; n) as n increases. Complete the following. (a) Write a function sS (x,n) that computes S(x; n). (b) Plot sinx on [0.4] together with the approximation S(x; 1). S(x; 2). S(x; 3). S(x; 6), and S(x 12)