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 3.52

Textbook Question

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

85.04°

Verified step by step guidance

Start with the formula to convert degrees to radians: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).

Substitute the given degree measure into the formula: \( 85.04 \times \frac{\pi}{180} \).

Simplify the expression by multiplying 85.04 by \( \frac{\pi}{180} \).

If necessary, use a calculator to compute the multiplication and division to get the radian measure.

Round the result to the nearest thousandth, if applicable.

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Key Concepts

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

Degree and Radian Measures

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 essential 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 corresponding value in radians, which is crucial for various applications in trigonometry.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of accuracy. In this context, when converting degrees to radians, the result may need to be rounded to the nearest thousandth, which involves looking at the digit in the fourth decimal place to determine whether to round up or down.

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