Answer:
B
Step-by-step explanation:
Using the trig. identity
cos x = [tex]\frac{1}{secx}[/tex]
Given
secx = - [tex]\frac{2\sqrt{3} }{3}[/tex] , then
cos x = - [tex]\frac{3}{2\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = - [tex]\frac{3\sqrt{3} }{6}[/tex] = - [tex]\frac{\sqrt{3} }{2}[/tex] , thus
x = [tex]cos^{-1}[/tex] (- [tex]\frac{\sqrt{3} }{2}[/tex] ) = [tex]\frac{5\pi }{6}[/tex] → B
