Question

Question

Find the exact value of cos 330°.

(1 point)
Responses

negative Start Fraction Start Root 3 End Root over 2 End Fraction
Image with alt text: negative Start Fraction Start Root 3 End Root over 2 End Fraction

negative Start Fraction Start Root 2 End Root over 2 End Fraction
Image with alt text: negative Start Fraction Start Root 2 End Root over 2 End Fraction

one-half
Image with alt text: one-half

Start Fraction Start Root 3 End Root over 2 End Fraction

Answer 1

To find the exact value of \(\cos 330^\circ\), we can utilize the properties of the unit circle and reference angles.

1. Determine the reference angle: The reference angle for \(330^\circ\) is \(360^\circ - 330^\circ = 30^\circ\).
2. Calculate the cosine: Since \(330^\circ\) is in the fourth quadrant, where cosine values are positive, we have: \[ \cos 330^\circ = \cos 30^\circ \]
3. 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).