(1)  108° = 90° + 18°.


     Use the trigonometric identity


         sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b).


     You will get


         sin(108°) = sin(90°+18°) = sin(90°)*cos(18°) + cos(90°)*sin(18°).   (*)


    Substitute here  sin(90°) = 1;  cos(90°) = 0;  sin(18°) = k  and  cos(18°) =  = .


    You will get then (by continuing (*) )


         sin(108°) =  +  = .     ANSWER



2.  cos(-36°)


    cos(-36°) = cos(36°) = cos(2*18°).


    Use the trigonometric identity


        cos(2a) = 1 - 2*sin^2(a).


    You will get then


        cos(-36°) = cos(36°) = cos(2*18°) = .      ANSWER