How many degrees are equivalent to $10$ radians?

• A. $10\times 57.3=573$ degrees
• B. $10\times \frac{180}{\pi }=572.96$ degrees
• C. $10\times \frac{\pi }{180}=0.1745$ degrees
• D. $10\times 90=900$ degrees

Answer: (B)

Verified step by step guidance

1. Recall the fundamental relationship between radians and degrees: \(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\).
2. To convert radians to degrees, multiply the number of radians by \(\frac{180}{\pi}\), so the formula is: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
3. Substitute the given value of radians (10 radians) into the formula: \(10 \times \frac{180}{\pi}\).
4. Set up the expression for calculation without simplifying: \(10 \times \frac{180}{\pi}\) degrees.
5. If needed, use the approximate value of \(\pi \approx 3.1416\) to evaluate the expression numerically, but keep the expression in fractional form for exactness.