Determine the solution(s) for the following where $0 \pi \leq \alpha \leq 2 \pi$ : $\cos (x)=-\frac{\sqrt{3}}{2}$
Answer
Final Answer: The solutions to the equation $\cos (x)=-\frac{\sqrt{3}}{2}$ are $\boxed{\frac{2\pi}{3}}$ and $\boxed{\frac{4\pi}{3}}$.
Step 1 ：Determine the solution(s) for the following where $0 \pi \leq \alpha \leq 2 \pi$ : $\cos (x)=-\frac{\sqrt{3}}{2}$
Step 2 ：The cosine function is negative in the second and third quadrants. The reference angle associated with $\cos(x) = -\frac{\sqrt{3}}{2}$ is $\frac{\pi}{6}$ (or 30 degrees).
Step 3 ：Therefore, the solutions to the equation are $\frac{2\pi}{3}$ and $\frac{4\pi}{3}$.
Step 4 ：Final Answer: The solutions to the equation $\cos (x)=-\frac{\sqrt{3}}{2}$ are $\boxed{\frac{2\pi}{3}}$ and $\boxed{\frac{4\pi}{3}}$.
