First, let’s analyze the given options and find which one corresponds to [tex]\(\tan 30^\circ\)[/tex].
1. Identify the possible values from the options:
- Option A: [tex]\(\frac{1}{2}\)[/tex]
- Option B: [tex]\(\frac{\sqrt{3}}{3}\)[/tex]
- Option C: [tex]\(\sqrt{2}\)[/tex]
2. Recall the trigonometric identity:
- For [tex]\(\tan 30^\circ\)[/tex], we know that:
[tex]\[
\tan 30^\circ = \frac{1}{\sqrt{3}}
\][/tex]
This can also be expressed in rationalized form:
[tex]\[
\tan 30^\circ = \frac{\sqrt{3}}{3}
\][/tex]
3. Compare the given options with the actual value of [tex]\(\tan 30^\circ\)[/tex]:
- Option A: [tex]\(\frac{1}{2}\)[/tex] – This does not match the expected value of [tex]\(\tan 30^\circ\)[/tex].
- Option B: [tex]\(\frac{\sqrt{3}}{3}\)[/tex] – This matches the expected value of [tex]\(\tan 30^\circ\)[/tex].
- Option C: [tex]\(\sqrt{2}\)[/tex] – This also does not match the expected value of [tex]\(\tan 30^\circ\)[/tex].
4. Calculation conclusion:
- Therefore, the correct option for [tex]\(\tan 30^\circ\)[/tex] is [tex]\(\frac{\sqrt{3}}{3}\)[/tex].
Conclusion:
The correct answer is [tex]\( \boxed{\frac{\sqrt{3}}{3}} \)[/tex]. This corresponds to Option B.
