Given an angle in standard position with its initial side along the positive $x$-axis and its terminal side passing through point $S$ on the unit circle, if the arc $QS$ subtends an angle of $120°$ at the origin, what is the measure of arc $QS$ in radians?

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $\frac{2\pi }{3}$

Answer: (D)

Verified step by step guidance

1. Recall that the measure of an arc on the unit circle in radians is equal to the measure of the central angle that subtends the arc.
2. Identify the given central angle measure in degrees, which is 120° in this problem.
3. Use the conversion formula from degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
4. Substitute 120° into the formula: \$120 \times \frac{\pi}{180}$.
5. Simplify the fraction \(\frac{120}{180}\) to \(\frac{2}{3}\), so the arc length in radians is \(\frac{2\pi}{3}\).