Plotting trigonometric, negative exponential functions

My question could be more related to math than Matlab, but since I want to plot them in matlab, I am asking it here.

I attached the functions that I'm trying to plot.

My Questions are:

1) why my trigonometric function is different from the attached? mine doesn't look like sine and cosine functions at all.

2) how to plot negative exponential function?

Here is my code:

t=1:1:100;
to=1;
th=t(end)-t(1);

b_l=0.2; a_l=1-b_l; % linear coeff
a_t=0.2; b_t=acos(2/a_t)/pi(); % trigonometric coeff
a_e = 0.2; b_e=-log(1/a_e); %exponential coeff

y1  = a_e * exp(-b_e*(t-to)/(th-to)); % exponential
y2  = a_l*((t-to)/(th-to)) + b_l; % linear 
y3  = (a_t/2)*( 1 + cos( (pi().*(t-to)*b_t)/(th-to) ) ); % Trigonometric 

figure(1);
plot(t,y1,'-k','LineWidth',3); hold on;
plot(t,y2,'-r','LineWidth',3); hold on;
plot(t,y3,'-m','LineWidth',3); hold on; 
legend('Exponential','Linear','Trigonometric','FontSize',14,'FontName','Time New Roman','Location','NorthWest');

[madhan ravi]

Post the actual exponential equation in mathematical form.

[John D'Errico]

@Mos_bad

Please don't answer your own question just to make a comment. Use a comment instead.

"Here are the math expressions that I found:

f_trigonometric (t) = (a/2) [1+cos( (πb (t-to))/(th- to )) ]

f_exponential (t)=a e^[(-b(t - to))/(th- to )]

and a and b are constants. the to and th in expression are equivalent to t0e and t0e+Tlc in attached figure, respectively.

And for negative exponential function, I don't have any math expression. I just found the attached plot in litrature.

0 Comments"

[Mos_bad]

Any body can help me with this?