1958 AHSME Problems/Problem 38

Problem

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:

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

Solution

$\fbox{}$

1958 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 37	Followed by Problem 39
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1958 AHSME Problems/Problem 38

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