proposition: Lemma sin_zero : sin 0 = 0.
proof: Proof. elim existence_AB_unitaire; intros A H; elim H; intros B H0; try clear H; try exact H0. elim existence_ROND_AB with (A := A) (B := B); [ intros D H | auto ]. elim H; intros. rewrite (def_sin (A:=A) (B:=B) (C:=B) (D:=D) (x:=0)); auto with geo. rewrite <- angle_nul; auto with geo. Qed.