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


42.5°

Verified step by step guidance

1. Understand that to convert degrees to radians, you use the conversion factor \( \frac{\pi}{180} \).
2. Multiply the degree measure by the conversion factor: \( 42.5 \times \frac{\pi}{180} \).
3. Simplify the expression by multiplying 42.5 by \( \frac{\pi}{180} \).
4. If necessary, round the result to the nearest thousandth.
5. Express the final answer in terms of \( \pi \) or as a decimal rounded to the nearest thousandth.

Key Concepts

Degree and Radian Measure

Degrees and radians are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. Understanding the relationship between these two units is crucial for converting angles from one measure to another.

Conversion Formula

To convert degrees to radians, the formula used is: radians = degrees × (π/180). This formula allows for the direct conversion of any angle measured in degrees to its equivalent in radians, facilitating calculations in trigonometry.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of accuracy. In this context, rounding to the nearest thousandth means keeping three decimal places. This is important for providing precise answers in mathematical calculations, especially in trigonometry.