Difference between revisions of "1958 AHSME Problems/Problem 38"

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== Problem ==
 
== Problem ==
Let <math> r</math> be the distance from the origin to a point <math> P</math> with coordinates <math> x</math> and <math> y</math>. Designate the ratio <math> \frac{y}{r}</math> by <math> s</math> and the ratio <math> \frac{x}{r}</math>  by <math> c</math>. Then the values of <math> s^2 \minus{} c^2</math> are limited to the numbers:
+
Let <math> r</math> be the distance from the origin to a point <math> P</math> with coordinates <math> x</math> and <math> y</math>. Designate the ratio <math> \frac{y}{r}</math> by <math> s</math> and the ratio <math> \frac{x}{r}</math>  by <math> c</math>. Then the values of <math> s^2 - c^2</math> are limited to the numbers:
  
<math> \textbf{(A)}\ \text{less than }{\minus{}1}\text{ are greater than }{\plus{}1}\text{, both excluded}\qquad\\
+
<math> \textbf{(A)}\ \text{less than }{-1}\text{ are greater than }{+1}\text{, both excluded}\qquad\\
\textbf{(B)}\ \text{less than }{\minus{}1}\text{ are greater than }{\plus{}1}\text{, both included}\qquad \\
+
\textbf{(B)}\ \text{less than }{-1}\text{ are greater than }{+1}\text{, both included}\qquad \\
\textbf{(C)}\ \text{between }{\minus{}1}\text{ and }{\plus{}1}\text{, both excluded}\qquad \\
+
\textbf{(C)}\ \text{between }{-1}\text{ and }{+1}\text{, both excluded}\qquad \\
\textbf{(D)}\ \text{between }{\minus{}1}\text{ and }{\plus{}1}\text{, both included}\qquad \\
+
\textbf{(D)}\ \text{between }{-1}\text{ and }{+1}\text{, both included}\qquad \\
\textbf{(E)}\ {\minus{}1}\text{ and }{\plus{}1}\text{ only}</math>
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\textbf{(E)}\ {-1}\text{ and }{+1}\text{ only}</math>
  
 
== Solution ==
 
== Solution ==

Latest revision as of 23:23, 13 March 2015

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

$\fbox{}$

See Also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 37
Followed by
Problem 39
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