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Step 1:I'll solve this step-by-step using precise LaTeX formatting:
Step 2:: Recall the Unit Circle Definition
The angle $$\frac{\pi}{6}$$ is a special angle in the unit circle.
It corresponds to 30 degrees, which has well-known trigonometric values.
Step 3:: Visualize the Angle
- The opposite side is $$\frac{1}{2}
- The adjacent side is \frac{\sqrt{3}}{2}
Step 4:: Trigonometric Definition
The tangent function is defined as $$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$$, which is equivalent to $$\frac{\text{opposite}}{\text{adjacent}}
Step 5:: Calculate the Value
\tan\left(\frac{\pi}{6}\right) = \frac{\sin\left(\frac{\pi}{6}\right)}{\cos\left(\frac{\pi}{6}\right)} = \frac{1/2}{\sqrt{3}/2} = \frac{1}{\sqrt{3}}
Step 6:: Simplify
\tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}
Final Answer
\tan\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{3}
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