function a1sol  %insert the exact file name (as explained in the submission
                           % instructions) after "function"

%------------------------------------------------------------------------
%%%               ENGINEERING MATHEMATICS III - MATH 2Z03
%%%                             ASSIGNMENT #1
%%%             HOMEWORK \#1: INTRODUCTION TO MATLAB
%------------------------------------------------------------------------


%------------------------------------------------------------------------
% Covers:
% - "Numerical Mathematics" by M. Grasselli and D. Pelinovsky,
%    Sections 1.1-1.6
% - "Advanced Engineering Mathematics" by D.G. Zill and W.S. Wright,
%    (Jones and Bartlett, 4th edition) Section 2.2
%------------------------------------------------------------------------


%------------------------------------------------------------------------
% Instructions:
% - Submit your assignment electronically (via Email) to the
%   address specific to your lab section as indicated on the course
%   website; hardcopy submissions will not be accepted.
% - It is obligatory to use the current MATLAB template file available at
%   http://www.math.mcmaster.ca/gabardo/M2Z03/frames/template.m; 
%   submissions non compliant with this template will not be accepted.
% - Make sure to enter your name and student I.D. number in the
%   appropriate section of the template.
% - Late submissions and submissions which do not comply with
%   these guidelines will not be accepted.
% - All graphs should contain suitable titles and legends.
%------------------------------------------------------------------------
% Written by Vladislav Bukshtynov, 2009

clc; close all; clear all;

% Student information
  
disp('  ------------   Student Information  ------------  ')  

% Please enter your information here
Name = 'Johny';
Surname = 'Good';
ID = 123456789;

fprintf('  Student:  %s %s (ID: %d) \n', Name, Surname, ID);



disp('  ------------------------------------------------  ')  
disp('  ')
disp('  ')
disp('  ')
disp('  ')


disp('  ----------   Solution to Question #1  ----------  ')  
disp('  ')
% Insert here your solution to Question #1
% (if you define your own functions, they may appear 
%  at the end of the file)
A=[6,7; 8, 9];
Answer1=matcos(A)
Answer2=matsin(A)
Answer3=(matcos(A))^2+(matsin(A))^2
disp('  ')
disp('  ------------------------------------------------  ')  
disp('  ')
disp('  ')
disp('  ')
disp('  ')

disp('  ----------   Solution to Question #2  ----------  ')  
disp('  ')
% Insert here your solution to Question #2
% (if you define your own functions, they may appear 
%  at the end of the file)

x=[-0.5:0.01:0.5];
y1=0.*x;
y2=asin(sqrt(3)/2*sqrt(x.^2+1));
y3=pi-asin(sqrt(3)/2*sqrt(x.^2+1));
y4=pi*ones(size(x));;
figure
plot(x,y1,x,y2,x,y3, x,y4);
xlabel('x'); ylabel('y');
grid on;
disp('  ')
disp('  ------------------------------------------------  ')  
disp('  ')
disp('  ')
disp('  ')
disp('  ')

disp('  ----------            Answers         ----------  ')  
disp('  ')
% DO NOT TOUCH THIS PART (RESERVED FOR THE INSTRUCTOR'S USE)

Name 
Surname 
ID

Answer1
Answer2
Answer3


function T=matcos(A)
T=0;
k=0;
while max(max(abs(A^(2*k)./factorial(2*k)))) >=0.01
T=T+(-1)^(k).*A^(2*k)./factorial(2*k);
k=k+1
end

function T=matsin(A)
T=0;
k=0;
while max(max(abs(A^(2*k+1)./factorial(2*k+1)))) >=0.01 
T=T+(-1)^(k).*A^(2*k+1)./factorial(2*k+1);
k=k+1
end