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


5

Verified step by step guidance

1. Identify the radian measure given in the problem. Here, the radian measure is 5 radians.
2. Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \dfrac{180}{\pi}\).
3. Multiply the given radian measure by \(\dfrac{180}{\pi}\) to convert it to degrees: \(5 \times \dfrac{180}{\pi}\).
4. Separate the decimal degree result into its whole number part (degrees) and the fractional part to convert the fraction into minutes. Remember, 1 degree = 60 minutes.
5. Multiply the fractional part of the degree by 60 to find the minutes, then round to the nearest minute as required.

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 more intuitive and commonly used in practical applications.

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 and rounding appropriately.

Rounding and Precision in Angle Measurement

When converting and expressing angles, rounding to the nearest minute ensures a balance between accuracy and simplicity. Understanding how to round decimal values correctly is crucial to provide precise and meaningful angle measurements.