To determine the exact value of [tex]\(\cos \left(\frac{\pi}{6}\right)\)[/tex], let's analyze the given information:
1. An angle of measure [tex]\(\frac{\pi}{6}\)[/tex] intersects the unit circle at the point [tex]\(\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\)[/tex].
2. In the unit circle, the coordinates of the point where an angle intersects the circle correspond to the [tex]\(\cos\)[/tex] (x-coordinate) and [tex]\(\sin\)[/tex] (y-coordinate) values of that angle.
Given:
[tex]\[ \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) \][/tex]
- The x-coordinate of this intersection point is [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
- Therefore, [tex]\(\cos \left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{\frac{\sqrt{3}}{2}} \][/tex]
