use the reference angle to find the exact value of the given expression. cos 23π/6 select the correct choice…

Explanation:

Step1: Find a coterminal angle

First, find a coterminal angle of $\frac{23\pi}{6}$ that is between $0$ and $2\pi$. We know that $\frac{23\pi}{6}=4\pi-\frac{\pi}{6}$. Since $4\pi$ is a full - rotation, $\cos(\frac{23\pi}{6})=\cos(4\pi - \frac{\pi}{6})$. According to the cosine difference formula $\cos(A - B)=\cos A\cos B+\sin A\sin B$, and for $A = 4\pi$ and $B=\frac{\pi}{6}$, $\cos(4\pi)=1$, $\sin(4\pi)=0$. So $\cos(4\pi-\frac{\pi}{6})=\cos\frac{\pi}{6}$.

Step2: Evaluate the cosine value

We know that for the angle $\theta=\frac{\pi}{6}$, $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}$.

Answer:

A. $\cos\frac{23\pi}{6}=\frac{\sqrt{3}}{2}$