Answer:
5π/6 and 7π/6
Explanation:
Using the inverse function of cosine, we get:
[tex]\begin{gathered} \text{cos x = }\frac{-\sqrt[]{3}}{2} \\ x=\cos ^{-1}(\frac{-\sqrt[]{3}}{2}) \\ x=\frac{5\pi}{6} \end{gathered}[/tex]
Then, cos(x) = cos(-x), so:
[tex]\cos (\frac{5\pi}{6})=\cos (\frac{-5\pi}{6})=\frac{-\sqrt[]{3}}{2}[/tex]
Finally, -5π/6 is also equivalent to 7π/6, because:
2π - 5π/6 = 7π/6
So, all the angles between o and 2π that satisfy the condition are:
5π/6 and 7π/6
