To determine the value of [tex]\(\cos 60^\circ\)[/tex], let's consider the properties of the cosine function and the unit circle as well as some well-known trigonometric values.
First, it's important to remember the basic angles and their respective cosine values:
- [tex]\(\cos 0^\circ = 1\)[/tex]
- [tex]\(\cos 30^\circ = \frac{\sqrt{3}}{2}\)[/tex]
- [tex]\(\cos 45^\circ = \frac{1}{\sqrt{2}}\)[/tex] or [tex]\(\frac{\sqrt{2}}{2}\)[/tex]
- [tex]\(\cos 60^\circ = \frac{1}{2}\)[/tex]
- [tex]\(\cos 90^\circ = 0\)[/tex]
We are asked to find [tex]\(\cos 60^\circ\)[/tex]. From the standard trigonometric values, we know that:
[tex]\[
\cos 60^\circ = \frac{1}{2}
\][/tex]
Thus, among the given choices:
A. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
B. 2
C. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
D. [tex]\(\frac{1}{2}\)[/tex]
E. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
F. [tex]\(\frac{2}{\sqrt{3}}\)[/tex]
The correct answer is:
D. [tex]\(\frac{1}{2}\)[/tex]
So, [tex]\(\cos 60^\circ\)[/tex] is [tex]\(\frac{1}{2}\)[/tex], and the corresponding choice is D.
