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


2

Verified step by step guidance

1. Identify the radian measure given in the problem. Since the problem states "2" without units, assume it means 2 radians.
2. Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \dfrac{180}{\pi}\).
3. Apply the formula by multiplying 2 radians by \(\dfrac{180}{\pi}\) to convert to degrees: \(2 \times \dfrac{180}{\pi}\).
4. Calculate the decimal value of the degrees (do not finalize the answer here, just note the step).
5. Convert the decimal degrees to degrees and minutes by separating the integer part (degrees) and multiplying the fractional part by 60 to get minutes, then round to the nearest 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 more intuitive and commonly used in practical applications.

Understanding Minutes in Angle Measurement

Degrees can be subdivided into minutes and seconds, where 1 degree equals 60 minutes. Writing answers to the nearest minute means expressing the angle in degrees and minutes, providing a more precise measurement than degrees alone.

Rounding and Precision in Angle Conversion

After converting radians to degrees, the decimal part must be converted into minutes by multiplying by 60. Proper rounding to the nearest minute ensures accuracy and clarity in the final answer, which is important for precise trigonometric calculations.