Difference between revisions of "2002 AIME II Problems/Problem 10"

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== Problem ==
 
== Problem ==
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While finding the sine of a certain angle, an absent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive real values of <math>x</math> for which the sine of <math>x</math> degrees is the same as the sine of <math>x</math> radians are <math>\frac{m\pi}{n-\pi}</math> and <math>\frac{p\pi}{q+\pi}</math>, where <math>m</math>, <math>n</math>, <math>p</math>, and <math>q</math> are positive integers. Find <math>m+n+p+q</math>.
  
 
== Solution ==
 
== Solution ==

Revision as of 14:02, 19 April 2008

Problem

While finding the sine of a certain angle, an absent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive real values of $x$ for which the sine of $x$ degrees is the same as the sine of $x$ radians are $\frac{m\pi}{n-\pi}$ and $\frac{p\pi}{q+\pi}$, where $m$, $n$, $p$, and $q$ are positive integers. Find $m+n+p+q$.

Solution

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See also

2002 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions