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MATH / An angle x is chosen at random from the interval 0^(∘)<x<90^(∘). Let p be the probability that the numbers sin²x, cos²x, and sinxcosx are not the lengths of the sides of a triangle…

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problem

An angle xx is chosen at random from the interval 0∘<x<90∘0^{\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.
Plain-text mathematical notation (without MathML)
An angle x is chosen at random from the interval 0^(∘)<x<90^(∘).  Let p be the probability that the numbers sin²x, cos²x, and sinxcosx are not the lengths of the sides of a triangle.  Given that p=d/n, where d is the number of degrees in arctanm and m and n are positive integers with m+n<1000, find m+n.
Original LaTeX notation
An angle $x$ is chosen at random from the interval $0^{\circ} < x < 90^{\circ}$.  Let $p$ be the probability that the numbers $\sin^2 x$, $\cos^2 x$, and $\sin x \cos x$ are not the lengths of the sides of a triangle.  Given that $p=d/n$, where $d$ is the number of degrees in $\arctan m$ and $m$ and $n$ are positive integers with $m+n<1000$, find $m+n$.

level

Level 5

type

Precalculus

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Source and history

task_id
571d49f2-de1c-5073-854f-4e8ce3ac4ad4
task_key
precalculus--test--571d49f2-de1c-5073-854f-4e8ce3ac4ad4
task_revision_id
1
config / split
precalculus / test

Official source

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