Question

Image 1 is the template that may help to solve this problem and it will serve as a guidline

81418lab1.m % I. Representation of a sine function using Taylor series [-2pi, 2pi] %% Part 1: Definition t = [-2*pi: .01,2*pi); of t - %% Part 2: Definition of y as a sine function of t -Y[1:length (t)l: %% Part 3: Generation of a plot of t and y figure: plot (t,y) hold on xlim(t (-2*pi) (2*pi) ]) ylim([-2 2]) xlabel ('t') ylabel ('y') %% Part 4: Taylor series method 1: Manual function [val] = sin t(t,n)! y2 ( (t^ (1) ) /factorial (1) )-( (t"(3) ) /factorial (3) ) + ( (t*S) ) /factoría end

Answer 1

(1) , (2), (3)

-----------------------------------sin_t.m----------------------------------

% calculate and return the value of sin(t)

% n is the number of terms in the series

function [val] = sin_t(t , n)

    val = 0;

   

    for i = 1 : n

       

        % calculate the i th term and add to val

        val = val + ( ( (-1) ^ ( i - 1 ) ) * ( t ^ ( 2 * i - 1 ) ) / factorial( 2 * i - 1 ) );

       

    end

end

---------------------main.m---------------------

% create a vector for time

t = [ -2 * pi : 0.01 : 2 * pi ];

% create a vector for same length as t to store the corresponding values of

% sin(t)

y = [ 1 : length(t) ];

for i = 1 : length(t)

   

    y(i) = sin_t( t(i) , 10 );

   

end

% set the label of axis

xlabel('t');

ylabel('sin(t)');

grid on

hold

% plot the graph

plot(t , y);

Sample Output

(4)

------------------------sin_t.m-----------------------

% calculate and return the value of sin(t)

% n is the number of terms in the series

function [val] = sin_t(t , n)

    % calculate the sum of n = 1 to 7

    val = ( ( t ^ ( 1 ) ) / factorial( 1 ) ) - ( ( t ^ ( 3 ) ) / factorial( 3 ) ) + ( ( t ^ ( 5 ) ) / factorial( 5 ) ) - ( ( t ^ ( 7 ) ) /factorial( 7 ) ) + ( ( t ^ ( 9 ) ) / factorial( 9 ) ) - ( ( t ^ ( 11 ) ) / factorial( 11 ) ) + ( ( t ^ ( 13 ) ) / factorial( 13 ) );

   

end

-------------------------main.m-------------------------

% create a vector for time

t = [ -2 * pi : 0.01 : 2 * pi ];

% create a vector for same length as t to store the corresponding values of

% sin(t)

y = [ 1 : length(t) ];

n = 13;

for i = 1 : length(t)

   

    y(i) = sin_t( t(i) );

   

end

% set the label of axis

xlabel('t');

ylabel('sin(t)');

grid on

hold

% plot the graph

plot(t , y);

Sample Output

(5)

-----------------------------------sin_t.m----------------------------------

% calculate and return the value of sin(t)

% n is the number of terms in the series

function [val] = sin_t(t , n)

    val = 0;

   

    for i = 1 : n

       

        % calculate the i th term and add to val

        val = val + ( ( (-1) ^ ( i - 1 ) ) * ( t ^ ( 2 * i - 1 ) ) / factorial( 2 * i - 1 ) );

       

    end

end

---------------------main.m--------------------

% create a vector for time

t = [ -2 * pi : 0.01 : 2 * pi ];

% create a vector for same length as t to store the corresponding values of

% sin(t)

y = [ 1 : length(t) ];

n = 13;

for i = 1 : length(t)

   

    y(i) = sin_t( t(i) , n );

   

end

% set the label of axis

xlabel('t');

ylabel('sin(t)');

grid on

hold

% plot the graph

plot(t , y);

Sample Output