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AMC12 2006b Test Paper
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Sample Question 24:

Let SS be the set of all points (x,y)(x,y) in the coordinate plane such that 0xπ20\leq x\leq \frac\pi 2 and 0yπ20\leq y\leq \frac\pi 2. What is the area of the subset of SS for which sin2xsinxsiny+sin2y34\sin^2 x - \sin x\sin y + \sin^2 y\le \frac 34?

(A) π29(B) π28(C) π26(D) 3π216(E) 2π29\mathrm{(A)}\ \frac {\pi^2}9 \qquad \mathrm{(B)}\ \frac {\pi^2}8 \qquad \mathrm{(C)}\ \frac {\pi^2}6 \qquad \mathrm{(D)}\ \frac {3\pi^2}{16} \qquad \mathrm{(E)}\ \frac {2\pi^2}9




Answer Keys

Question 24: C