Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
39°
691
views
1. Measuring Angles
Complementary and Supplementary Angles
Problem 51
Textbook Question
Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).
64.29°
Verified step by step guidance1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(64.29^\circ \times \frac{\pi}{180}\).
Multiply the degree value by \(\pi\) to get \(64.29 \times \pi\) in the numerator.
Divide the result by 180 to complete the conversion to radians.
If needed, use a calculator to approximate the value and round the result to the nearest thousandth.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Degree to Radian Conversion
Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many trigonometric calculations.
Recommended video:
5:04
Converting between Degrees & Radians
Use of π in Radian Measures
Radians are often expressed in terms of π to maintain exact values. For example, 180° equals π radians. Understanding how to represent angles using π helps in simplifying and interpreting trigonometric expressions.
Recommended video:
5:04Converting between Degrees & Radians
Rounding to the Nearest Thousandth
When converting degrees to radians, the result may be an irrational number. Rounding to the nearest thousandth means limiting the decimal places to three digits, which balances precision and simplicity for practical use.
Recommended video:
4:45How to Use a Calculator for Trig Functions
Related Videos
Related Practice