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


3.06

Verified step by step guidance

1. Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \dfrac{180}{\pi}\).
2. Substitute the given radian measure into the formula: \(3.06 \times \dfrac{180}{\pi}\).
3. Calculate the decimal degree value from the multiplication (do not round yet).
4. Separate the decimal degree value into its whole number part (degrees) and the fractional part.
5. Convert the fractional part of the degree into minutes by multiplying it by 60, then round to the nearest whole minute.

Key Concepts

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. Expressing angles in degrees and minutes provides a more precise measurement than decimal degrees.

Rounding to the Nearest Minute

After converting radians to degrees and minutes, rounding to the nearest minute involves approximating the fractional part of the minutes to the closest whole number. This ensures the answer is both accurate and practical for use.