2003 AIME I Problem 11


An angle xx is chosen at random from the interval 0<x<900^\circ < x < 90^\circ. Let pp be the probability that the numbers sin2x\sin^2 x, cos2x\cos^2 x, and sinxcosx\sin x \cos x are not the lengths of the sides of a triangle. Given that p=d/np = d/n, where dd is the number of degrees in arctanm\arctan m and mm and nn are positive integers with m+n<1000m + n < 1000, find m+nm + n.


Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

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Problem Tags: Trigonometry

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Category: AIME I
Points: 5
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