Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

9.84763

검증된 단계별 안내

Recall the conversion formula between radians and degrees: \(\text{degrees} = \text{radians} \times \dfrac{180}{\pi}\).

Multiply the given radian measure, 9.84763, by \(\dfrac{180}{\pi}\) to convert it to degrees: \(9.84763 \times \dfrac{180}{\pi}\).

Calculate the decimal degree value from the multiplication (do not round yet).

Separate the decimal degree value into its whole number part (degrees) and the fractional part (decimal minutes).

Convert the fractional part of the degrees to minutes by multiplying it by 60, then round the result to the nearest whole number to get the minutes.

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주요 개념

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Radian to Degree Conversion

Radians and degrees are two units for measuring angles. To convert radians to degrees, multiply the radian measure by 180/π. This conversion is essential because degrees are often easier to interpret in practical contexts.

Degrees, Minutes, and Seconds

Degrees can be subdivided into minutes and seconds, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. Writing answers to the nearest minute means converting the decimal part of degrees into minutes by multiplying by 60.

Rounding to the Nearest Minute

After converting the decimal degrees to minutes, rounding to the nearest minute involves approximating the fractional minutes to the closest whole number. This ensures the angle measurement is precise and easy to communicate.

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).9.84763