Find the exact value of cos 330°.

Question

(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 use the fact that \(330^\circ\) is in the fourth quadrant. The reference angle for \(330^\circ\) is \(360^\circ - 330^\circ = 30^\circ\).

The cosine function is positive in the fourth quadrant, and we can use the cosine of the reference angle:

\[ \cos(330^\circ) = \cos(30^\circ) \]

The exact value of \(\cos(30^\circ)\) is

\[ \frac{\sqrt{3}}{2} \]

Thus, we have:

\[ \cos(330^\circ) = \frac{\sqrt{3}}{2} \]

The correct response is:

\[ \frac{\sqrt{3}}{2} \]