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


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Verified step by step guidance

1. Understand that to convert radians to degrees, you use the conversion factor \( \frac{180}{\pi} \).
2. Multiply the given radian measure by \( \frac{180}{\pi} \) to convert it to degrees. For example, multiply 5 by \( \frac{180}{\pi} \).
3. Calculate the product to get the degree measure in decimal form.
4. Separate the decimal part from the whole number to convert the decimal degrees into minutes. Multiply the decimal part by 60 to find the minutes.
5. Round the minutes to the nearest whole number to get the final answer in degrees and minutes.

Key Concepts

Radian to Degree Conversion

To convert radians to degrees, use the formula: degrees = radians × (180/π). This relationship stems from the definition of a radian, which is based on the radius of a circle. Understanding this conversion is essential for solving problems that require angle measurements in different units.

Understanding Minutes in Angles

In angle measurement, a degree can be further divided into minutes, where 1 degree equals 60 minutes. This subdivision allows for more precise measurements of angles. When converting radians to degrees, it is important to express the final answer in degrees and minutes, especially when specified in the problem.

Precision in Measurement

Precision refers to the level of detail in a measurement. In this context, converting to the nearest minute means rounding the degree measurement to the closest minute value. This concept is crucial for ensuring that answers meet the required accuracy, particularly in fields that rely on precise angle measurements.