To solve $\cos \left( \frac{\pi}{6} \right)$ using the unit circle provided in the image:

1. The unit circle represents the cosine and sine values for standard angles, with the x-coordinate corresponding to the cosine of the angle and the y-coordinate to the sine of the angle.
2. $\frac{\pi}{6}$ radians is one of the key angles, and it corresponds to 30 degrees.
3. On the unit circle, the coordinates for $\frac{\pi}{6}$ are $\left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right)$.
4. Since cosine corresponds to the x-coordinate, we have: $\cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2}$

Thus, $\cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2}$.

Would you like further details on this, or do you have any questions?

Here are 5 related questions you can try:

1. What is $\sin \left( \frac{\pi}{6} \right)$?
2. Find $\cos \left( \frac{\pi}{4} \right)$ using the unit circle.
3. What is the value of $\cos \left( \frac{\pi}{3} \right)$?
4. Can you compute $\tan \left( \frac{\pi}{6} \right)$?
5. How do you calculate $\sin \left( \frac{5\pi}{6} \right)$ using the unit circle?

Tip: On the unit circle, the cosine values mirror symmetrically across the y-axis, and sine values mirror across the x-axis!