Difference between revisions of "2006 AIME I Problems/Problem 12"
(cos(5x) solutions were incorrect) |
|||
Line 11: | Line 11: | ||
[[Category:Intermediate Trigonometry Problems]] | [[Category:Intermediate Trigonometry Problems]] | ||
+ | {{MAA Notice}} |
Revision as of 20:06, 4 July 2013
Problem
Find the sum of the values of such that
, where
is measured in degrees and
Solution
Observe that by the sum-to-product formulas. Defining
and
, we have
. But
, so we require
,
,
, or
.
Hence the solution set is and thus
.
See also
2006 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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.