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Convert the angle -1 radian to degrees, rounding to the nearest 10th. Answer:

Convert the angle −1-1 radian to degrees, rounding to the nearest 1010th.\newlineAnswer:

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Full solution

Q. Convert the angle −1-1 radian to degrees, rounding to the nearest 1010th.\newlineAnswer:
  1. Convert to degrees: To convert radians to degrees, we use the conversion factor that π\pi radians is equivalent to 180180 degrees. The formula to convert radians to degrees is: degrees=radians×(180π)\text{degrees} = \text{radians} \times (\frac{180}{\pi}).
  2. Substitute value: Now, we substitute −1-1 for radians in the formula: degrees=−1×(180/π)\text{degrees} = -1 \times (180/\pi).
  3. Perform multiplication: Perform the multiplication to find the degree measure: degrees=−180π\text{degrees} = \frac{-180}{\pi}.
  4. Calculate decimal value: Using a calculator, we find the decimal value of −180/π-180/\pi, which is approximately −57.2958-57.2958 degrees.
  5. Round to nearest tenth: Finally, we round the result to the nearest tenth: degrees ≈−57.3\approx -57.3.

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