[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]
[tex]\sf C) \quad \left(\dfrac{4\pi}{3}, \sqrt{3}\right)[/tex]
Step-by-step explanation:
[tex]\huge\mathbb{ \underline{GIVEFUNCTION:}}[/tex]
[tex]y=\cot x \implies y=\dfrac{1}{\tan x}y=cotx[/tex]
Substitute the x-values of the given coordinates into the given function:
[tex]\textsf{}\:x=\dfrac{5 \pi}{6}: \quad y=\dfrac{1}{\tan \left(\dfrac{5 \pi}{6}\right)}=\dfrac{1}{-\dfrac{\sqrt{3}}{3}}=-\sqrt{3}[/tex]
[tex]\textsf{}\:x=\dfrac{7 \pi}{4}: \quad y=\dfrac{1}{\tan \left(\dfrac{7 \pi}{4}\right)}=\dfrac{1}{-1}=-1[/tex]
[tex]\textsf{}\:x=\dfrac{4 \pi}{3}: \quad y=\dfrac{1}{\tan \left(\dfrac{4 \pi}{3}\right)}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]
Comparing the y-values of the given coordinates, we can clearly see that point that is not on the graph of the function is:
[tex]\sf \left(\dfrac{4\pi}{3}, \sqrt{3}\right)[/tex]