10. 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.
$10 . y=\sin x$ is a periodic wave with values in $[-1,1]$. Imagine a circle with a sufficiently large radius that is tangent to the $x$-axis at the origin; it will intersect the sine wave many times. The larger the radius, the greater the number of intersections can be.
(E) True.