1. Convince yourself (using the Maclaurin Series Equation from p. 19) that the Maclaurin Series for sin(x) is: sin(x) x - x3/3! + x*/5!- x2k-1 .. 4i (2k -1)! (n-term approximation) k-1 2. Write a function M-file called sine_series that takes as its inputs x and n and has output given by the sum in the n-term Maclaurin Series approximation for sin(x). Hint: try a "for loop": for k - 1:n and set: "format long" in your code. 3. Check your code for problem 2 by finding the one-term, 3-term, and 5-term Maclaurin Series approximations for sin(/6) and for sin (T/3). Check your 3-term approximation for sin(T/6) "by hand." (It's OK to use MATLAB in your check, in the interactive mode.)