**il3.) The number of radians in a \( 480^{\circ} \) angle can be written as \( m \pi \) radians, where \( m \) is a constant. What is the value of \( m \) ? a. 4 b. \( \frac{8}{3} \) c. 2 d. \( \frac{9}{4} \)

1. We know that to convert degrees to radians, we use the formula: \[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \] 2. For a \(480^\circ\) angle, substitute: \[ \text{radians} = 480 \times \frac{\pi}{180} \] 3. Simplify the fraction: \[ \frac{480}{180} = \frac{48}{18} = \frac{8}{3} \] Thus, the angle in radians is: \[ \frac{8}{3}\pi \] 4. Comparing with the expression \( m\pi \), we find: \[ m = \frac{8}{3} \] The correct answer is \( \frac{8}{3} \).