2002 AIME II Problems/Problem 10
Revision as of 03:25, 6 December 2019 by Greenpizza96 (talk | contribs)
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 for which the sine of
degrees is the same as the sine of
radians are
and
, where
,
,
, and
are positive integers. Find
.
Solution
Note that degrees is equal to
radians. Also, for
, the two least positive angles
such that
are
, and
.
Clearly for positive real values of
.
yields:
.
yields:
.
So, .
See also
2002 AIME II (Problems • Answer Key • Resources) | ||
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.