**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. $$ \frac{9}{4} $$

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UpStudy AI · Accepted Answer

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 $$ \frac{8}{3} $$.
$$ m = \frac{8}{3} $$

**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. \( \frac{9}{4} \)

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