#Exercise 1. Make a function convert_angle(t, p) that takes an angle t and parameter p. Zero value of p indicates that the angle t is in degrees, and the function should return the value of the angle in radians; value p = 1 indicates that the angle t is in radians, and the function should return the measure of this angle in degrees. def convert_angle(t,p): ... ######################## #Exercise 4. Make a figure similar to Fig. 10.4 in Chapter 10 for the sum cos(3 Pi*t)+cos(2.7 Pi*t). #The exercise is similar to the example about beats in Chapter 10. ######################## #Exercise 6. Make a CAS function acoef(f(x), n) that takes two inputs, a piecewise differentiable 2π-periodic function and an integer n and returns a list of n+1 Fourier coefficients a[k], k=0, 1, ..., n, of the function f. #Use the formula for a[k] calculation in Chapter 10. ####################### #Exercise 7. Make a CAS function bcoef(f(x), n) that takes two arguments, a piecewise differentiable 2π-periodic function and an integer n and returns a list of n Fourier coefficients b[k], k=1, 2, ..., n, of the function f. #Use the formula for b[k] calculation in Chapter 10. ####################### #Exercise 8. Consider the 2π-periodic function f(x) = abs(x), x in [-Pi, Pi] (triangular wave function). #(a) Find three partial sums S__n, n=3, 4, 6, of the Fourier series for this function #(b) Make three figures, each with the pairs of graphs f, and one of the partial sums S__n`, n=3, 4, 6, over three periods. ####################### #Exercise 10. #(a) Construct the Fourier series for the function g(t) = sin(t) for 0<=0<pi, g(t)=0 for pi<= t < 2*Pi. #Directions: Use your functions in Exercise 6 and Exercise 7 to find several Fourier coefficients a[k] and b[k]. By visual inspection, determine the pattern and write the Fourier series. #(b) Plot the function and its partial Fourier series in one figure.