3 years ago

18 points

Mathematics

1 answer:

bearhunter [10]3 years ago

4 0

12 is first one 7 is 2nd one 9 is the last one

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Which is an asymptote of the graph of the function y = cot ( x - 2pi / 3 )

vesna_86 [32]

$\bf y=cot\left(x-\frac{2\pi }{3} \right)\implies y=\cfrac{cos\left(x-\frac{2\pi }{3} \right)}{sin\left(x-\frac{2\pi }{3} \right)}$

now, if the denominator turns to 0, the fraction becomes undefined, and you get a "vertical asymptote" when that happens, so let's check when is that

$\bf sin\left(x-\frac{2\pi }{3} \right)=0\implies sin^{-1}\left[ sin\left(x-\frac{2\pi }{3} \right) \right]=sin^{-1}(0)
\\\\\\
x-\frac{2\pi }{3}=
\begin{cases}
0\\
\pi 
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{2\pi }{3}\\
\frac{5\pi }{3}
\end{cases}$

now, at those angles, the function is asymptotic, check the picture below