(b)

% From (a) y = -cos(x) + 1 represents the probability that a signal's duration is between 0 and x
% We will plot this function again, and a line at x = pi/4 to answer (b)
% You only need two points to plot a line for x = pi/4, how would you do it?
x = 0 : 0.001 : pi/2;
y = -cos(x) + 1;
figure;
hold on;
plot(x,y);
plot([pi/4 pi/4], [0 1]); % This plots a line between (pi/4, 0) and (pi/4, 1)
% The intersection between these two graphs is the answer
xlabel('x'); ylabel('Probability of signal duration less than x'); title('Cumulative Distributive Function of x');
hold off;

% -----EXTRA-----

t = 0 : 0.001 : pi/2;
x = 0 : 0.001 : pi/4;
f = sin(t);
fx = sin(x);
figure;
hold on;
plot(t, f);
area(x, fx);
xlabel('t'); title('Probability Density Function')
hold off;
% Area is the answer to the question

% ---------------

x = pi/4; % Redefine x to be the point of interest
y = -cos(x) + 1 % This answer is not suppressed so the result is printed out