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 3.9

Textbook Question

Convert each degree measure to radians. Leave answers as multiples of π.

800°

Verified step by step guidance

Convert the degree measure to radians using the formula: radians = degrees \times \frac{\pi}{180}

Substitute 800° into the formula: radians = 800 \times \frac{\pi}{180}

Simplify the fraction \frac{800}{180} by finding the greatest common divisor of 800 and 180.

Express the simplified fraction as a multiple of \pi.

Write the final expression as a multiple of \pi, leaving it in terms of \pi.

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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 conversion factor π radians = 180 degrees. This means that to convert a degree measure to radians, you multiply the degree value by π/180. For example, to convert 800°, you would calculate 800 × (π/180).

Simplifying Fractions

After converting degrees to radians, it is often necessary to simplify the resulting fraction. This involves reducing the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, in the case of 800/180, both numbers can be divided by 20 to simplify the fraction.

Understanding π in Trigonometry

In trigonometry, π (pi) is a fundamental constant representing the ratio of a circle's circumference to its diameter. It is crucial in expressing angles in radians, as many trigonometric functions are defined in terms of radians rather than degrees. Recognizing π as a key component in radian measures helps in understanding the relationships between angles and their corresponding trigonometric values.