8.45 An arbitrary circle and the curve $y=\sin x$ can intersect at
(A) at most 2 points.
(B) at most 4 points.
(C) at most 6 points.
(D) at most 8 points.
(E) more than 16 points.
(36th American High School Mathematics Examination, 1985)
［Solution］For a circle with its center on the $y$-axis, an extremely large radius (at which point the arc of the circle is nearly a straight line), and capable of intersecting with $y=\sin x$, the number of intersection points can be infinitely many (as shown in the figure). Therefore, the answer is $(E)$.