what are all the exact solutions of cos x = -√3/2 on the interval π≤x≤2π? give your answer in radians. o π/6…

Explanation:

Step1: Recall cosine - value knowledge

We know that $\cos\theta =-\frac{\sqrt{3}}{2}$ has general solutions $\theta = 2k\pi\pm\frac{5\pi}{6},k\in\mathbb{Z}$.

Step2: Find solutions in given interval

We want solutions in the interval $\pi\leq x\leq2\pi$. When we consider the general form, for $k = 1$: If we take $\theta=2\pi-\frac{5\pi}{6}=\frac{12\pi - 5\pi}{6}=\frac{7\pi}{6}$ and $\theta = 2\pi+\frac{5\pi}{6}$ is out of the given interval, and when we consider $\theta = 2\pi-\frac{7\pi}{6}=\frac{5\pi}{6}$ is also out of the given interval. The only solution of $\cos x=-\frac{\sqrt{3}}{2}$ in the interval $\pi\leq x\leq2\pi$ is $x = \frac{7\pi}{6}$.

Answer:

$\frac{7\pi}{6}$