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Convert the angle -1.5 radians to degrees, rounding to the nearest 10 th. Answer:

Convert the angle −1-1.55 radians to degrees, rounding to the nearest 1010th.\newlineAnswer:

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Full solution

Q. Convert the angle −1-1.55 radians to degrees, rounding to the nearest 1010th.\newlineAnswer:
  1. Conversion Factor Application: 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 \left(\frac{180}{\pi}\right). Now, let's apply this formula to −1.5-1.5 radians.
  2. Multiplication Step: First, we multiply −1.5-1.5 by the conversion factor 180π\frac{180}{\pi}:degrees=−1.5×(180π).\text{degrees} = -1.5 \times \left(\frac{180}{\pi}\right).
  3. Calculation: Using a calculator, we find the value: degrees≈−1.5×(180/3.141592653589793)≈−85.94366926962348\text{degrees} \approx -1.5 \times (180/3.141592653589793) \approx -85.94366926962348.
  4. Rounding: Now, we round this value to the nearest tenth: degrees≈−85.9\text{degrees} \approx -85.9.

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