To determine the value of [tex]\(\cos 60^\circ\)[/tex], we need to recall some fundamental trigonometric values. These values can be derived from the unit circle and are often memorized because of their frequent use.
The cosine of an angle in trigonometry represents the x-coordinate of the point on the unit circle that corresponds to that angle. Specifically:
- For [tex]\(\theta = 60^\circ\)[/tex], the corresponding point on the unit circle is [tex]\(\left(\cos 60^\circ, \sin 60^\circ\right)\)[/tex].
From trigonometric tables or the unit circle, we know that:
- [tex]\(\cos 60^\circ = \frac{1}{2}\)[/tex]
Now, let's match this value with the provided options:
- A. [tex]\(\frac{2}{\sqrt{3}}\)[/tex]
- B. [tex]\(\frac{1}{2}\)[/tex]
- C. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
- D. 2
- E. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
- F. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
From the options given, [tex]\(\frac{1}{2}\)[/tex] matches the known value of [tex]\(\cos 60^\circ\)[/tex].
Thus, the correct answer is:
B. [tex]\(\frac{1}{2}\)[/tex]
