Difference between revisions of "2002 AMC 12P Problems/Problem 25"
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| − | Let <math>a</math> and <math>b</math> be real numbers such that <math>\sin{a} + \sin{b} = \sqrt{2}{2}</math> and <math>\cos {a} + \cos {b} = \sqrt{6}{2}.</math> Find <math>\sin{(a+b)}.</math> | + | Let <math>a</math> and <math>b</math> be real numbers such that <math>\sin{a} + \sin{b} = \frac{\sqrt{2}}{2}</math> and <math>\cos {a} + \cos {b} = \frac{\sqrt{6}}{2}.</math> Find <math>\sin{(a+b)}.</math> |
<math> | <math> | ||
Revision as of 00:27, 30 December 2023
Problem
Let 
and 
be real numbers such that 
and 
Find 
Solution
If 
, then 
. Since 
, must be 
to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of 
.
See also
| 2002 AMC 12P (Problems • Answer Key • Resources) | |
| Preceded by Problem 24 |
Followed by Last question |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
