(*****************************************************************)
(** * Using series definitions of cos and sin                    *)
(*****************************************************************)

Definition sin_lb (a:R) : R := sin_approx a 3.Definition sin_ub (a:R) : R := sin_approx a 4.Definition cos_lb (a:R) : R := cos_approx a 3.Definition cos_ub (a:R) : R := cos_approx a 4.

Lemma sin_lt_0 : forall x:R, PI < x -> x < 2 * PI -> sin x < 0.