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


-5.01095

Verified step by step guidance

1. Recall the conversion factor between radians and degrees: $1 ext{ radian} = \frac{180}{\pi} ext{ degrees}$.
2. Multiply the given radian measure by the conversion factor: $-5.01095 \times \frac{180}{\pi}$.
3. Calculate the product to convert the radian measure to degrees.
4. Separate the decimal part from the whole number part of the degree measure.
5. Convert the decimal part of the degree measure to minutes by multiplying by 60, and round to the nearest minute.

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 the angle subtended at the center of a circle by an arc equal in length to the radius. Understanding this conversion is essential for accurately translating angular measurements.

Understanding Minutes in Angles

In angular measurement, a degree can be subdivided 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 instructed to round to the nearest minute.

Negative Angles

Negative angles indicate a rotation in the clockwise direction, as opposed to the counterclockwise direction of positive angles. When converting a negative radian measure to degrees, the same conversion process applies, but the resulting degree measure will also be negative. This concept is crucial for understanding the orientation of angles in trigonometric contexts.