Bounded geodesics in manifolds of negative curvature

Let M be a complete Riemannian manifold with sectional curvature less than or equal to -1 and dimension greater than or equal to 3. Given a unit vecto r v is an element of T-1 M and a point x is an element of M we prove the ex istence of a complete geodesic through x whose tangent vector never comes c lose to v. As a consequence we show the existence of a bounded geodesic thr ough every point in a complete negatively pinched manifold with finite volu me and dimension greater than or equal to 3.