evaluate the expression cos⁻¹(sin(5π/6)). give your answer as an exact value question help: video 1 video 2…

Explanation:

Step1: Find the value of $\sin(\frac{5\pi}{6})$

We know that $\sin(\frac{5\pi}{6})=\sin(\pi - \frac{\pi}{6})$. Since $\sin(A - B)=\sin A\cos B-\cos A\sin B$ and $\sin(\pi - \alpha)=\sin\alpha$, then $\sin(\frac{5\pi}{6})=\sin(\frac{\pi}{6})=\frac{1}{2}$.

Step2: Evaluate $\cos^{-1}(\frac{1}{2})$

Let $\theta=\cos^{-1}(\frac{1}{2})$, then $\cos\theta=\frac{1}{2}$ and $\theta\in[0,\pi]$. We know that $\cos(\frac{\pi}{3})=\frac{1}{2}$, so $\theta = \frac{\pi}{3}$.

Answer:

$\frac{\pi}{3}$