Question

Problem 1 (10 pts) (Matlab coding)

In this problem you will be manipulating a sine wave plot using a for loop and if statements.

1. a) Create a vector x that goes from −4π to 4π with increments of π/10.

2. b) Instead of using y = sin(x) on the entire array at once, use a for loop to calculate the sine of x for each value in the vector individually. Vector y should be the sine of vector x. Use the following formula as a hint on how to set up your for loop, where yi is the ith element of y and xi is the ith element of x:

   yi = sin(xi)

3. c) Now, we will be manipulating the sine wave. We want to take all of the negative values of the sine wave and make them positive. You should use an if statement inside your for loop to re-assign the negative y-values to be equal to the corresponding positive value of y. To do this, you can use the following formula inside your if statement:

   yi = abs(yi)

   Only use abs() on yi if yi is negative.

4. d) Next, we will be clipping the sine wave to stay between 0 and 0.8 on the y-axis. To do this, you should use another if statement inside your for loop to take any y-values greater than 0.8 and set them equal to 0.8.

5. e) Outside of your for loop, plot sin(x) vs. x. Now, plot y vs. x (which is the manipulated sine wave) on the same plot. Your plot should look like the one below. Add axis-labels and a legend to match the plot below.

Problem 2 (10 pts)

In this this problem you will be using for loops to take a matrix of random number and create a new matrix that is the same as the random matrix, but with zeros on the diagonal.

1. a) Create matrix m that is a 10x10 matrix of random whole numbers from 1 to 20. You will have to manipulate the random number generator function to modify the interval and get only whole numbers.

2. b) Create a for loop that runs for index i equal to the index for every row in the matrix. Next, create a nested for loop that runs for index j equal to the index for every column in the matrix. This is very similar to the Your Turn - Extra slide of Lecture 13.

3. c) Now, we want to use our for loops to create a new matrix, n, that is equal to matrix m, but with zeros on the diagonal. You should use an if/else statement to create this new matrix. If the location is on the diagonal (i=j), then the value of matrix n at the location will be zero. Otherwise, the value of matrix n equals the value of matrix m at each location.

4. d) Display matrices m and n on separate lines using the disp() function. You should get something like this in your Command Window. The numbers you generate will not be the same, but this is the basic format:

Answer 1

First Part-

Code

x = -4*pi:pi/10:4*pi;

y = [];

for i = x
   yi = sin(i);
   if (yi < 0)
       yi = abs(yi);
   endif
   if (yi > 0.8)
       yi = 0.8;
   endif
   y = [y yi];
endfor

figure;
plot(x, sin(x));
hold on;
plot(x, y);
legend("sin(x)", "y");
xlabel("x");
ylabel("sin(x)");

OUTPUT-

Second Part-

code-

x = randi([1 20],10);

y = zeros(size(x));

for i = 1:size(x, 1)
   for j = 1:size(x, 2)
       if (i == j)
           y(i, j) = 0;
       else
           y(i, j) = x(i, j);
endif
endfor
endfor
disp("x-");
disp(x);
disp("y-");
disp(y);

OUTPUT-

I hope it helps. For any doubt, feel free to ask in comments, and give upvote if u get the answer.