To determine the exact value of $\cos\left(\frac{5\pi}{6}\right)$ using reference angles, follow these steps:

Step 1: Identify the quadrant

The angle $\frac{5\pi}{6}$ is in the second quadrant because:

• $\frac{5\pi}{6}$ is greater than $\frac{\pi}{2}$ and less than $\pi$.

Step 2: Find the reference angle

The reference angle $\theta_r$ is the acute angle formed with the x-axis. For an angle $\theta$ in the second quadrant, the reference angle is: $\theta_r = \pi - \theta$ Substituting $\theta = \frac{5\pi}{6}$: $\theta_r = \pi - \frac{5\pi}{6} = \frac{\pi}{6}$

Step 3: Use the cosine of the reference angle

The cosine of the reference angle $\frac{\pi}{6}$ is: [ \cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{