Difference between revisions of "2006 AMC 12B Problems/Problem 24"
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== Problem == | == Problem == | ||
| − | {{ | + | Let <math>S</math> be the set of all point <math>(x,y)</math> in the coordinate plane such that <math>0 \le x \le \frac{\pi}{2}</math> and <math>0 \le y \le \frac{\pi}{2}</math>. What is the area of the subset of <math>S</math> for which |
| + | |||
| + | <cmath> | ||
| + | \sin^2x-\sin x \sin y + \sin^2y \le \frac34? | ||
| + | </cmath> | ||
| + | |||
| + | <math> | ||
| + | \mathrm{(A)}\ \dfrac{\pi^2}{9} | ||
| + | \qquad | ||
| + | \mathrm{(B)}\ \dfrac{\pi^2}{8} | ||
| + | \qquad | ||
| + | \mathrm{(C)}\ \dfrac{\pi^2}{6} | ||
| + | \qquad | ||
| + | \mathrm{(D)}\ \dfrac{3\pi^2}{16} | ||
| + | \qquad | ||
| + | \mathrm{(E)}\ \dfrac{2\pi^2}{9} | ||
| + | </math> | ||
== Solution == | == Solution == | ||
Revision as of 22:09, 16 April 2009
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Problem
Let 
be the set of all point 
in the coordinate plane such that 
and 
. What is the area of the subset of for which
![\[\sin^2x-\sin x \sin y + \sin^2y \le \frac34?\]](http://latex.artofproblemsolving.com/d/b/f/dbfe47d3cebb8cec2ec7292989a766db924380a7.png)
Solution
See also
| 2006 AMC 12B (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 | |
