value: 2 use the unit circle to find cos⁻¹(-√3/2) in radians. remember that the domain of inverse cosine is…

Explanation:

Step1: Recall cosine - unit circle relationship

We know that $\cos\theta=x$ on the unit - circle, where $(x,y)$ is a point on the unit - circle and $\theta$ is the angle measured counter - clockwise from the positive $x$ - axis. We need to find $\theta$ such that $\cos\theta =-\frac{\sqrt{3}}{2}$ and $0\leq\theta\leq\pi$.

Step2: Analyze cosine values in quadrants I and II

In the unit - circle, $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}$. Since we want $\cos\theta =-\frac{\sqrt{3}}{2}$ and the cosine function is negative in the second quadrant ($\frac{\pi}{2}<\theta\leq\pi$), and we know that $\cos(\pi - \alpha)=-\cos\alpha$. Let $\alpha=\frac{\pi}{6}$, then $\cos(\pi-\frac{\pi}{6})=\cos\frac{5\pi}{6}=-\frac{\sqrt{3}}{2}$.

Answer:

D. $\frac{5\pi}{6}$