Trouble in getting analytic and numeric solution for integrating sine wave

Hello everyone,

I'm trying to get coordinates for a robot movement from a sine wave. Now I changed the length of one period and the last and most important plot looks aweful. Does anyone can explain what's wrong in my code? I'm using Matlab R2020b for academic use.

clear;

% Distance

t = 0.05; % Frequency

A = 50;  %Amplitude

x = 0:t:10*pi;
y = A*sin(x);       %It's all good if I leave sin(x), but when I want to change the duration of one period, like 2x
                    %the plot looks like in the picture.

T = (1:length(x))*t;

figure(1)
plot(T,y,'.')
xlabel('time')
ylabel('distance')
%%
vel = gradient(y)./gradient(x);

figure(2)
plot(T,vel,'.')
xlabel('time')
ylabel('velocity')
%%
acc = gradient(vel)./gradient(x);
  
figure(3)
plot(T,acc,'.')
xlabel('time')
ylabel('acceleration')

acc = acc';
%xlswrite('Acceleration.xlsx',acc);
acc = acc';
%%
%velocity Cosinus Figure

v = zeros(1,length(acc));

v(1,1) = A * cos(0);

l_v = 1:length(acc);

for i = 2:length(l_v)
    
    v(i) = ((acc(i)+acc(i-1))/2) * t + v(i-1);
    
end

figure(4)
scatter(T,v,'.')
xlabel('time')
ylabel('velocity')

v = v';
%xlswrite('Velocity.xlsx',v);
v = v';

%%
%distance Sinus Figure

s = zeros(1,length(v));

s(1,1) = sin(0);

for i = 2:length(acc)
    
    s(i) = ((v(i)+v(i-1))/2) * t + s(i-1);
    
end


figure(5)
scatter(T,s,'.')

xlabel('time')
ylabel('distance')

s = s';

%xlswrite('idealwaves.xlsx',s)

[Walter Roberson]

Your velocity is already wrong: look at its range.

[Bruce Rogers]

Hello Walter,

I don't see the mistake, why is my range wrong?

[Bruce Rogers]

Hey Walter,

I just saw the range of the velocity, its starts at 50 and ends at -150 (－‸ლ)

Thanks for the hint, I just changed

v(1,1) = A * cos(0);

to

v(1,1) = 2 * A * cos(0);

and it looks fine for me.