1958 AHSME Problem 38

Let r be the distance from the origin to a point P with coordinates x and y. Designate the ratio \frac{y}{r} by s and the ratio \frac{x}{r} by c. Then the values of s^2 - c^2 are limited to the numbers:

\begin{array}{l} \textbf{(A)}\ \text{less than }{-1}\text{ are greater than }{+1}\text{, both excluded}\qquad\\ \textbf{(B)}\ \text{less than }{-1}\text{ are greater than }{+1}\text{, both included}\qquad \\ \textbf{(C)}\ \text{between }{-1}\text{ and }{+1}\text{, both excluded}\qquad \\ \textbf{(D)}\ \text{between }{-1}\text{ and }{+1}\text{, both included}\qquad \\ \textbf{(E)}\ {-1}\text{ and }{+1}\text{ only} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.