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Convert the angle -4.5 radians to degrees, rounding to the nearest 10th. Answer:

Convert the angle −4-4.55 radians to degrees, rounding to the nearest 1010th.\newlineAnswer:

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Full solution

Q. Convert the angle −4-4.55 radians to degrees, rounding to the nearest 1010th.\newlineAnswer:
  1. Understand radians and degrees: Understand the relationship between radians and degrees. One radian is equal to 180/π180/\pi degrees. To convert radians to degrees, we multiply the radian measure by 180/π180/\pi.
  2. Convert −4.5-4.5 radians: Convert −4.5-4.5 radians to degrees.\newlineTo convert −4.5-4.5 radians to degrees, we multiply −4.5-4.5 by 180π\frac{180}{\pi}.\newlineCalculation: (−4.5(-4.5 radians) * (180π)\left(\frac{180}{\pi}\right) degrees/radian) = −4.5×180/π-4.5 \times 180/\pi degrees
  3. Perform calculation: Perform the calculation.\newlineUsing a calculator, we find that −4.5×180/π-4.5 \times 180/\pi is approximately −257.5959-257.5959 degrees.
  4. Round to nearest 1010th: Round the result to the nearest 1010th. Rounding −257.5959-257.5959 to the nearest 1010th gives us −257.6-257.6 degrees.

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