To determine the value of [tex]\(\cos 30^\circ\)[/tex], we need to evaluate the cosine of a 30-degree angle.
We know from trigonometry that:
[tex]\[
\cos 30^\circ = \frac{\sqrt{3}}{2}
\][/tex]
Let's compare this value to the given options:
A. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
[tex]\[
\frac{1}{\sqrt{3}} \approx 0.577
\][/tex]
B. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
[tex]\[
\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \approx 0.707
\][/tex]
C. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
[tex]\[
\frac{\sqrt{3}}{2} \approx 0.866
\][/tex]
D. [tex]\(\frac{1}{2}\)[/tex]
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
E. 1
[tex]\[
1.0
\][/tex]
F. [tex]\(\sqrt{3}\)[/tex]
[tex]\[
\sqrt{3} \approx 1.732
\][/tex]
The value [tex]\(0.8660254037844387\)[/tex] found from the cosine of 30 degrees matches option C:
[tex]\[
\frac{\sqrt{3}}{2} \approx 0.8660254037844387
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{\sqrt{3}}{2}}
\][/tex]
