Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
39°

Verified step by step guidance

1. Understand that to convert degrees to radians, you use the conversion factor \( \frac{\pi}{180} \).
2. Set up the conversion by multiplying the degree measure by \( \frac{\pi}{180} \).
3. For 39°, write the expression as \( 39 \times \frac{\pi}{180} \).
4. Simplify the expression by multiplying 39 by \( \frac{\pi}{180} \).
5. If necessary, round the result to the nearest thousandth.

Key Concepts

Degree to Radian Conversion

To convert degrees to radians, use the formula: radians = degrees × (π/180). This relationship arises 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 Radians

A radian is a unit of angular measure defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. Since there are 2π radians in a full circle (360 degrees), radians provide a natural way to describe angles in mathematical contexts, especially in calculus and trigonometry.

Rounding Numbers

Rounding is the process of adjusting the digits of a number to reduce its precision while maintaining its value as close as possible. In this context, rounding to the nearest thousandth means keeping three decimal places. This is important for presenting answers clearly and concisely, especially in scientific and engineering applications.