Question

Find all angles between 0 and 2pi satisfying the condition.

Answer 1

5π/6 and 7π/6

Step-by-step explanation:

Using the inverse function of cosine, we get:

`\begin{gathered} \text{cos x = }\frac{-\sqrt[]{3}}{2} \\ x=\cos ^(-1)(\frac{-\sqrt[]{3}}{2}) \\ x=(5\pi)/(6) \end{gathered}`

Then, cos(x) = cos(-x), so:

`\cos ((5\pi)/(6))=\cos ((-5\pi)/(6))=\frac{-\sqrt[]{3}}{2}`

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