How to draw a variable width line?

I'm trying to draw a line that has a variable width over time. In the below, i make it go from 1 to 20 and back to 1 over 200 steps. Is this even possible? If so, what am I doing wrong?

X = linspace(1,300,3000);
Y = linspace(1,300,3000);
Y = sin(Y);
% plot(X,Y,'LineWidth', 2) % PLOTS SINE WAVE WITH LINEWIDTH OF 2

qnum = 100;
    qsp = 2;
    qz = round([linspace(1,qsp,qnum) linspace(qsp,1,qnum)]);
    while size(qz) < 3000
        qz = [qz qz];
    end
    for qq = 1:3000
        plot(X(qq),Y(qq),'LineWidth',qz(qq))
    end

Answer 1

[KSSV]

qnum = 300 ; 
X = linspace(0,2*pi,qnum);
Y = sin(X);

qsp = 10;
qz = round(linspace(1,qsp,qnum-1));

figure
hold on
for qq = 1:qnum-1
    plot(X(qq:qq+1),Y(qq:qq+1),'LineWidth',qz(qq),'color','k')
end