What is the reference angle of the angle \( \frac{5 \pi}{3} ? \) \( \frac{-\pi}{2} \) \( \frac{-\pi}{3} \) \( \frac{\pi}{3} \)

To find the **reference angle** for \( \frac{5\pi}{3} \), follow these steps: 1. **Understand the Position of the Angle:** - \( \frac{5\pi}{3} \) radians is equivalent to 300 degrees. - This angle lies in the **fourth quadrant** of the unit circle, where angles range from \( \frac{3\pi}{2} \) (270 degrees) to \( 2\pi \) (360 degrees). 2. **Calculate the Reference Angle:** - The reference angle is the smallest angle between the terminal side of the given angle and the x-axis. - For angles in the fourth quadrant, the reference angle can be found by subtracting the angle from \( 2\pi \): \[ \text{Reference Angle} = 2\pi - \frac{5\pi}{3} = \frac{6\pi}{3} - \frac{5\pi}{3} = \frac{\pi}{3} \] 3. **Select the Correct Option:** - Among the given choices: - \( \frac{-\pi}{2} \) is not a reference angle. - \( \frac{-\pi}{3} \) is negative and reference angles are always positive. - \( \frac{\pi}{3} \) is the correct reference angle. **Answer:** \( \frac{\pi}{3} \)