Answer:
option 1
2sqrt3/3
Step-by-step explanation:
Given in the question
csc(-4π/3)
we know that csc(x) = [tex]\frac{1}{sin(x)}[/tex] that means
[tex]csc(\frac{-4\pi}{3})=\frac{1}{sin(\frac{-4\pi}{3} )}[/tex]
sin(-4π/3) = [tex]\frac{\sqrt{3}}{2}[/tex]
so,
[tex]csc(\frac{-4\pi}{3})=\frac{1}{\frac{\sqrt{3}}{2} }[/tex]
[tex]\frac{1}{\sqrt{3}/2 }[/tex] = [tex]\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}[/tex]
