What is [tex]\cos 30^{\circ}[/tex]?

A. [tex]\frac{1}{\sqrt{3}}[/tex]
B. [tex]\frac{1}{\sqrt{2}}[/tex]
C. [tex]\frac{\sqrt{3}}{2}[/tex]
D. [tex]\frac{1}{2}[/tex]
E. 1
F. [tex]\sqrt{3}[/tex]



Answer :

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]