Pregunta
**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. \( \frac{9}{4} \)
Ask by Chan Ball. in the United States
Mar 18,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( m = \frac{8}{3} \)
Solución
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 \( \frac{8}{3} \).
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Beyond the Answer
To convert degrees to radians, you can use the formula \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \). For \( 480^{\circ} \), it would be \( 480 \times \frac{\pi}{180} = \frac{480\pi}{180} = \frac{8\pi}{3} \). So in this case, \( m = \frac{8}{3} \). Thus, the correct answer is \( b. \frac{8}{3} \).

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