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Convert the angle -2 radians to degrees, rounding to the nearest 10 th. Answer:

Convert the angle −2-2 radians to degrees, rounding to the nearest 1010th.\newlineAnswer:

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Full solution

Q. Convert the angle −2-2 radians to degrees, rounding to the nearest 1010th.\newlineAnswer:
  1. Conversion Formula: To convert radians to degrees, we use the conversion factor that π \pi radians is equal to 180180 degrees. The formula to convert radians to degrees is:\newlineDegrees=Radians×(180π) \text{Degrees} = \text{Radians} \times \left( \frac{180}{\pi} \right) \newlineNow, we will apply this formula to convert −2-2 radians to degrees.
  2. Substitute Radians: Substitute −2-2 for the radians in the conversion formula:\newlineDegrees=−2×(180π) \text{Degrees} = -2 \times \left( \frac{180}{\pi} \right)
  3. Perform Multiplication: Perform the multiplication to find the degree measure:\newlineDegrees=−2×(180π)≈−2×57.2958≈−114.5916 \text{Degrees} = -2 \times \left( \frac{180}{\pi} \right) \approx -2 \times 57.2958 \approx -114.5916
  4. Round Result: Round the result to the nearest tenth:\newlineDegrees≈−114.6 \text{Degrees} \approx -114.6

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