I wrote the program as follows (my second ti basic program) for the ti 84 ce

for(x,0,360,15)
x store to y
sin(y) store to L
disp "sin",L,"degrees",y
pause
end


I tried the frac function, but according to my research and experience it does not work inti basic
It works fine, I am trying to have my vales as correct values (ex (sqrt3)/2 instead of ,8660254038I now that the program still needs a lot of finishing touches.

What you're looking for is called an "exact math engine", and it turns out that the French version of the 84 Plus CE (the "TI-83 Premium CE") has this exact feature... meaning that you'll get values with the square roots etc. instead of approx values.
Sadly enough, the 84+CE doesn't have that so you'll have to use some kind of lookup table / list that knows the approx values and gives you back the hardcoded exact value.

There exist exact math engine programs, though. For example CEXP (which I've just tested on a 84+CE, it works there too)

Unit circle programs also exist. For example DynaTrig:

And probably many more here.

But anyway, you're encouraged to make yours too, it's a good exercise to learn how to code that