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 3.47

Textbook Question

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

42.5°

Verified step by step guidance

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

Multiply the degree measure by the conversion factor: \( 42.5 \times \frac{\pi}{180} \).

Simplify the expression by multiplying 42.5 by \( \frac{\pi}{180} \).

If necessary, round the result to the nearest thousandth.

Express the final answer in terms of \( \pi \) or as a decimal rounded 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 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.