Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).


56° 25'

Verified step by step guidance

1. Convert the degree measure to a decimal by recognizing that 25' (minutes) is a fraction of a degree. Since there are 60 minutes in a degree, convert 25' to degrees by dividing by 60: \( 25' = \frac{25}{60} \) degrees.
2. Add the converted minutes to the degree measure: \( 56° + \frac{25}{60}° \).
3. Calculate the total degree measure as a decimal.
4. Use the conversion factor from degrees to radians: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).
5. Multiply the total degree measure by \( \frac{\pi}{180} \) to convert it to radians.

Key Concepts

Degree to Radian Conversion

To convert degrees to radians, use the formula: radians = degrees × (π/180). 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 solving problems that require angle measurements in different units.

Understanding Minutes in Angles

In angle measurement, degrees can be subdivided into minutes and seconds, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This means that when converting angles expressed in degrees and minutes to radians, both components must be converted separately before summing them. Recognizing this subdivision is crucial for accurate conversions.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of accuracy, often to simplify calculations or present results clearly. In this context, rounding to the nearest thousandth means keeping three decimal places in the final answer. Mastery of rounding techniques is important for ensuring that results are both precise and easy to interpret.