Certainly! Let's determine the quadrant where the angle [tex]\(\frac{2 \pi}{3}\)[/tex] terminates.
1. Convert the Angle from Radians to Degrees:
The angle [tex]\(\frac{2 \pi}{3}\)[/tex] is given in radians. To convert it to degrees, we use the conversion factor [tex]\(180^\circ = \pi\)[/tex] radians.
[tex]\[
\frac{2 \pi}{3} \text{ radians} \times \frac{180^\circ}{\pi} = \frac{2 \cdot 180^\circ}{3} = 120^\circ
\][/tex]
2. Determine the Quadrant:
The next step is to determine in which quadrant the angle [tex]\(120^\circ\)[/tex] lies. The unit circle is divided into four quadrants:
- Quadrant I: [tex]\(0^\circ \leq \theta < 90^\circ\)[/tex]
- Quadrant II: [tex]\(90^\circ \leq \theta < 180^\circ\)[/tex]
- Quadrant III: [tex]\(180^\circ \leq \theta < 270^\circ\)[/tex]
- Quadrant IV: [tex]\(270^\circ \leq \theta < 360^\circ\)[/tex]
Since [tex]\(120^\circ\)[/tex] lies between [tex]\(90^\circ\)[/tex] and [tex]\(180^\circ\)[/tex], it falls in Quadrant II.
So, the angle [tex]\(\frac{2 \pi}{3}\)[/tex] or [tex]\(120^\circ\)[/tex] terminates in Quadrant II.
The correct answer is II.
