Difference between revisions of "2007 AMC 12A Problems/Problem 24"
(New page: == Problem == For each integer <math>n>1</math>, let <math>F(n)</math> be the number of solutions to the equation <math>\sin{x}=\sin{(nx)}</math> on the interval <math>[0,\pi]</math>. Wha...) |
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For each integer <math>n>1</math>, let <math>F(n)</math> be the number of solutions to the equation <math>\sin{x}=\sin{(nx)}</math> on the interval <math>[0,\pi]</math>. What is <math>\sum_{n=2}^{2007} F(n)</math>? | For each integer <math>n>1</math>, let <math>F(n)</math> be the number of solutions to the equation <math>\sin{x}=\sin{(nx)}</math> on the interval <math>[0,\pi]</math>. What is <math>\sum_{n=2}^{2007} F(n)</math>? | ||
| − | <math>\mathrm{(A)}\ 2014524 \mathrm{(B)}\ 2015028 \mathrm{(C)}\ 2015033 \mathrm{(D)} | + | <math>\mathrm{(A)}\ 2014524</math> <math>\mathrm{(B)}\ 2015028</math> <math>\mathrm{(C)}\ 2015033</math> <math>\mathrm{(D)}\ 2016532</math> <math>\mathrm{(E)}\ 2017033</math> |
== Solution == | == Solution == | ||
Revision as of 19:29, 28 September 2007
Problem
For each integer 
, let 
be the number of solutions to the equation 
on the interval ![$[0,\pi]$](http://latex.artofproblemsolving.com/e/c/e/ece27ba559bd93cdf2416aa0f88fc8d7d85e5791.png)
. What is 
?
Solution
By looking at various graphs, we obtain that
See also
| 2007 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 23 |
Followed by Problem 25 |
| 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 | |
