What is the exact value of $\tan (300°)$?

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

Answer: (C)

Verified step by step guidance

1. Recall that the tangent function has a period of 180°, so \( \tan(300^\circ) = \tan(300^\circ - 180^\circ) = \tan(120^\circ) \).
2. Identify the reference angle for 120°, which is \( 180^\circ - 120^\circ = 60^\circ \).
3. Determine the sign of \( \tan(120^\circ) \) by considering the quadrant: 120° lies in the second quadrant where tangent is negative.
4. Use the known exact value \( \tan(60^\circ) = \sqrt{3} \).
5. Combine the sign and reference angle value to write \( \tan(300^\circ) = -\sqrt{3} \).