What is the value of $\tan \frac{\pi }{3}$ on the unit circle?

• A. $1$
• B. $0$
• C. $\sqrt{3}$
• D. $\frac{1}{\sqrt{3}}$

Answer: (C)

Verified step by step guidance

1. Recall that the tangent function on the unit circle is defined as \(\tan \theta = \frac{\sin \theta}{\cos \theta}\), where \(\theta\) is the angle in radians.
2. Identify the angle given: \(\theta = \frac{\pi}{3}\). This corresponds to 60 degrees, a common special angle in trigonometry.
3. Recall the sine and cosine values for \(\frac{\pi}{3}\): \(\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}\) and \(\cos \frac{\pi}{3} = \frac{1}{2}\).
4. Substitute these values into the tangent formula: \(\tan \frac{\pi}{3} = \frac{\sin \frac{\pi}{3}}{\cos \frac{\pi}{3}} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\).
5. Simplify the fraction by dividing the numerators and denominators accordingly to find the exact value of \(\tan \frac{\pi}{3}\).