Difference between revisions of "1992 AIME Problems/Problem 11"
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== Problem == | == Problem == | ||
| + | Lines <math>l_1^{}</math> and <math>l_2^{}</math> both pass through the origin and make first-quadrant angles of <math>\frac{\pi}{70}</math> and <math>\frac{\pi}{54}</math> radians, respectively, with the positive x-axis. For any line <math>l^{}_{}</math>, the transformation <math>R(l)^{}_{}</math> produces another line as follows: <math>l^{}_{}</math> is reflected in <math>l_1^{}</math>, and the resulting line is reflected in <math>l_2^{}</math>. Let <math>R^{(1)}(l)=R(l)^{}_{}</math> and <math>R^{(n)}(l)^{}_{}=R\left(R^{(n-1)}(l)\right)</math>. Given that <math>l^{}_{}</math> is the line <math>y=\frac{19}{92}x^{}_{}</math>, find the smallest positive integer <math>m^{}_{}</math> for which <math>R^{(m)}(l)=l^{}_{}</math>. | ||
== Solution == | == Solution == | ||
Revision as of 21:37, 10 March 2007
Problem
Lines 
and 
both pass through the origin and make first-quadrant angles of 
and 
radians, respectively, with the positive x-axis. For any line 
, the transformation 
produces another line as follows: is reflected in , and the resulting line is reflected in . Let 
and 
. Given that is the line 
, find the smallest positive integer 
for which 
.
Solution
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