4. Using elementary geometry and the definition of sin x, cos x, one can show for every x, y E R (see Appendix B) that

(i) I sinxl :::; 1, I cosxl :::; 1, sin(O) = 0, cos(O) = 1,

(ii) sin(-x) = -sinx, cos(-x) = cos x,

(iii) sin2 x + cos2 X = 1, cos x = 1- 2sin2~,

Moreover, if x is measured in radians, then (v)
and (vi)
cosx = sin (i -x) , 0< xcosx < sin x < x, sinx = cos (i -x) , 7r 0< x:S 2·