To find the value of [tex]\(\cos 60^\circ\)[/tex], let's break down the steps involved:
1. Understanding the Angle: We need to determine the cosine of an angle, specifically [tex]\(60^\circ\)[/tex].
2. Knowledge of Special Angles: In trigonometry, certain angles such as [tex]\(30^\circ\)[/tex], [tex]\(45^\circ\)[/tex], and [tex]\(60^\circ\)[/tex] are well-known, and their trigonometric values are worth memorizing because of their frequent use and simplicity.
3. Identify the Exact Value:
- [tex]\(\cos 60^\circ = \frac{1}{2}\)[/tex]
Having found that [tex]\(\cos 60^\circ = \frac{1}{2}\)[/tex], let's match this against the provided choices:
A. [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
B. [tex]\(\sqrt{3}\)[/tex]
C. [tex]\(\frac{1}{2}\)[/tex]
D. 1
E. [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
F. [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
Clearly, the correct choice that matches [tex]\(\cos 60^\circ\)[/tex] is:
C. [tex]\(\frac{1}{2}\)[/tex]
