To determine the value of [tex]\(\cos 60^{\circ}\)[/tex], follow these steps:
1. Understanding the Question:
We need to find the cosine of [tex]\(60\)[/tex] degrees and compare it with the given options.
2. Cosine of Specific Angles:
In trigonometry, certain angles, particularly those in the first quadrant, have well-known cosine values. [tex]\(60\)[/tex] degrees is one of these special angles.
3. Identifying Options:
The given options are:
- [tex]\( \frac{1}{2} \)[/tex]
- [tex]\( \frac{\sqrt{3}}{2} \)[/tex]
- [tex]\( \sqrt{3} \)[/tex]
- [tex]\( \frac{1}{\sqrt{2}} \)[/tex]
- [tex]\( 1 \)[/tex]
- [tex]\( \frac{1}{\sqrt{3}} \)[/tex]
4. Known Value of [tex]\(\cos 60^{\circ}\)[/tex]:
From trigonometric tables or the unit circle, it is established that the cosine of [tex]\(60^{\circ}\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
5. Matching with the Options:
Evaluate the options to find the value [tex]\(\frac{1}{2}\)[/tex]:
- Option A: [tex]\( \frac{1}{2} \)[/tex]
- Option B: [tex]\( \frac{\sqrt{3}}{2} \)[/tex]
- Option C: [tex]\( \sqrt{3} \)[/tex]
- Option D: [tex]\( \frac{1}{\sqrt{2}} \)[/tex]
- Option E: [tex]\( 1 \)[/tex]
- Option F: [tex]\( \frac{1}{\sqrt{3}} \)[/tex]
6. Conclusion:
The value [tex]\(\frac{1}{2}\)[/tex] is present as Option A.
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{1}{2}} \][/tex]
