To determine [tex]\(\cos 30^{\circ}\)[/tex], we can use our knowledge of the properties of trigonometric functions and the unit circle.
The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. However, for common angles, such as [tex]\(30^{\circ}\)[/tex], [tex]\(45^{\circ}\)[/tex], and [tex]\(60^{\circ}\)[/tex], there are standard values that we should know.
The angle [tex]\(30^{\circ}\)[/tex] is well-known, and its cosine value can be recalled from trigonometric tables or unit circle relations. In particular:
[tex]\[
\cos 30^{\circ} = \frac{\sqrt{3}}{2}
\][/tex]
Now let's match this with the given answer choices:
A. 1
B. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
C. [tex]\(\frac{1}{2}\)[/tex]
D. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
E. [tex]\(\sqrt{3}\)[/tex]
F. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
Clearly, the correct choice is:
B. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
This means that [tex]\(\cos 30^{\circ} = \frac{\sqrt{3}}{2}\)[/tex], which approximately equals [tex]\(0.8660254037844386\)[/tex].
