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Double/Half Angle Identities (Trigonometry)

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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 lenghts of the sides of the sides of a triangle. Given that $p=\frac{d}{n}$, where $d$ is the number of degrees in $arctan(m)$ and $m$ and $n$ are positive integers such that $m+n<1000$, what is $m+n$?

Apr 2, 2021

2+0 Answers

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p = arctan(3)/60, so m + n = 63.

Apr 2, 2021
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Hi Guest! It says the answer is incorrect, but it hasn't given me the correct answer yet, can you show your full work and I can look for errors? Thanks!

RiemannIntegralzzz  Apr 2, 2021