if function is going towards any number   

 then if that fuction's right & left limits and its value at that any number are same then you can say that that fuction is continue at that number.

 

exe  f(x) = { x    x<0

                { x^2   x>=0             find its continutity at x=0

 

here  lim   x = 0        and     lim   x^2 = 0       f(0) = 0     

        x-->0-                         x-->0+

thus we can say it is continue at x=0

we can find it for trigo function by this methord. for that you can select any interval. if that fuction is continue in that interval then above methord will right for it.