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 3.13

Textbook Question

Convert each radian measure to degrees.

8π/3

Verified step by step guidance

Understand the relationship between radians and degrees: 1 radian = 180/π degrees.

To convert a radian measure to degrees, multiply the radian value by 180/π.

Apply the conversion formula to the given radian measure: $ \frac{8\pi}{3} \times \frac{180}{\pi} $.

Simplify the expression by canceling out $ \pi $ from the numerator and denominator.

Multiply the remaining numbers to find the degree measure.

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Key Concepts

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

Radian and Degree Measures

Radians and degrees 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 radians to degrees, the formula used is: degrees = radians × (180/π). This formula allows for the straightforward conversion of any angle measured in radians to its equivalent in degrees, facilitating easier calculations and comparisons.

Simplifying Fractions

When converting angles, it is often necessary to simplify fractions. This involves reducing the fraction to its lowest terms, which can make calculations easier and help in understanding the angle's measure more clearly. For example, simplifying 8π/3 may involve recognizing that it can be expressed in terms of a full circle.