To find the exact value of \(\cos 330^\circ\), we can utilize the properties of the unit circle and reference angles.
- Determine the reference angle: The reference angle for \(330^\circ\) is \(360^\circ - 330^\circ = 30^\circ\).
- Calculate the cosine: Since \(330^\circ\) is in the fourth quadrant, where cosine values are positive, we have: \[ \cos 330^\circ = \cos 30^\circ \]
- Find \(\cos 30^\circ\): The value of \(\cos 30^\circ\) is \(\frac{\sqrt{3}}{2}\).
Thus, the exact value of \(\cos 330^\circ\) is:
\[ \cos 330^\circ = \frac{\sqrt{3}}{2} \]
The correct response is:
\(\frac{\sqrt{3}}{2}\) (which corresponds to the last option in your list).