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%% 1 & 2
%runs functions and tests for part 1 of the assignment
clear all;
close all;
clc;


x = (-1 * pi):0.1:pi;
y = f_d1(x);


plot(x, y)
hold on
plot((pi / 4), f_d1(pi / 4), 'ro') %checks theoretical root 1
plot((-pi / 4), f_d1(-pi / 4), 'ro') % checks theoretical root 2
xlabel('$$ \theta $$', 'Interpreter', 'latex')
ylabel('$$ f(\theta) $$', 'Interpreter', 'latex')
grid on

disp('f(pi / 4) yields:')
disp(f_d1(pi / 4))
disp('f(- pi / 4) yields:')
disp(f_d1(-pi / 4))

%% 3

close all;
clear all;
clc;

u1 = 1;
u2 = 2;
u3 = 2;
v1 = 2;
v2 = 1;
v3 = 3;

x1 = 4;
x2 = 0;
y2 = 4;

subplot(1,2,1);
plot([u1 u2 u3 u1],[v1 v2 v3 v1],'r'); hold on
plot([0 x1 x2],[0 0 y2],'bo');
plot([0 u1], [0 v1],'b');
plot([4 u2], [0 v2],'b');
plot([0 u3], [4 v3],'b');


u3 = 3;
v3 = 2;

subplot(1,2,2);
plot([u1 u2 u3 u1],[v1 v2 v3 v1],'r'); hold on
plot([0 x1 x2],[0 0 y2],'bo');
plot([0 u1], [0 v1],'b');
plot([4 u2], [0 v2],'b');
plot([0 u3], [4 v3],'b');