Answer :
To find the value of [tex]\(\cos 30^{\circ}\)[/tex], we can follow these steps:
1. Understand the problem: We need to determine which of the given options is equal to [tex]\(\cos 30^{\circ}\)[/tex].
2. Convert the angle to radians (since cosine is typically calculated in radians):
[tex]\[ 30^{\circ} = \frac{30 \pi}{180} = \frac{\pi}{6} \][/tex]
3. Recall the exact value of [tex]\(\cos \frac{\pi}{6}\)[/tex]:
[tex]\(\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}\)[/tex]
4. Match this value with the provided options:
- Option A: [tex]\(\sqrt{3}\)[/tex]
- Option B: [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
- Option C: [tex]\(\frac{\sqrt{3}}{2}\)[/tex] [tex]\(\ \checkmark\ \)[/tex] (This matches our exact value)
- Option D: [tex]\(\frac{1}{2}\)[/tex]
- Option E: 1
- Option F: [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
So, [tex]\(\cos 30^{\circ} = \frac{\sqrt{3}}{2}\)[/tex], which corresponds to Option C.
Thus, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
1. Understand the problem: We need to determine which of the given options is equal to [tex]\(\cos 30^{\circ}\)[/tex].
2. Convert the angle to radians (since cosine is typically calculated in radians):
[tex]\[ 30^{\circ} = \frac{30 \pi}{180} = \frac{\pi}{6} \][/tex]
3. Recall the exact value of [tex]\(\cos \frac{\pi}{6}\)[/tex]:
[tex]\(\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}\)[/tex]
4. Match this value with the provided options:
- Option A: [tex]\(\sqrt{3}\)[/tex]
- Option B: [tex]\(\frac{1}{\sqrt{2}}\)[/tex]
- Option C: [tex]\(\frac{\sqrt{3}}{2}\)[/tex] [tex]\(\ \checkmark\ \)[/tex] (This matches our exact value)
- Option D: [tex]\(\frac{1}{2}\)[/tex]
- Option E: 1
- Option F: [tex]\(\frac{1}{\sqrt{3}}\)[/tex]
So, [tex]\(\cos 30^{\circ} = \frac{\sqrt{3}}{2}\)[/tex], which corresponds to Option C.
Thus, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
