(** Definition of cosinus *)
Definition sin_n (n:nat) : R := (-1) ^ n / INR (fact (2 * n + 1)).

Lemma sin_no_R0 : forall n:nat, sin_n n <> 0.
Definition sin_in (x l:R) : Prop :=
infinite_sum (fun i:nat => sin_n i * x ^ i) l.