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 3.11

Textbook Question

Convert each radian measure to degrees.

5π/4

Verified step by step guidance

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

Identify the given radian measure: $ \frac{5\pi}{4} $.

Multiply the radian measure by $ \frac{180}{\pi} $ to convert it to degrees: $ \frac{5\pi}{4} \times \frac{180}{\pi} $.

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

Perform the multiplication and division 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 or 2π radians. To convert between these units, the relationship is established: 180 degrees equals π radians. Understanding this relationship is essential for converting radian measures to degrees.

Conversion Formula

The conversion from radians to degrees can be performed using the formula: degrees = radians × (180/π). This formula allows for straightforward calculations when converting any radian measure into its equivalent degree measure, ensuring accuracy in the conversion process.

Understanding π

The symbol π (pi) represents a mathematical constant approximately equal to 3.14159. It is crucial in trigonometry and geometry, particularly in calculations involving circles. Recognizing how π relates to angles and its role in the conversion process is vital for solving problems involving radian measures.