Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Complementary and Supplementary Angles

Trigonometry

1. Measuring Angles

Complementary and Supplementary Angles

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Problem 3.45

Textbook Question

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

Verified step by step guidance

Understand that to convert degrees to radians, you use the conversion factor $ \frac{\pi}{180} $.

Set up the conversion by multiplying the degree measure by $ \frac{\pi}{180} $.

For 39°, write the expression as $ 39 \times \frac{\pi}{180} $.

Simplify the expression by multiplying 39 by $ \frac{\pi}{180} $.

If necessary, round the result to the nearest thousandth.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.