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 3.5

Textbook Question

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

45°

Verified step by step guidance

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

Substitute 45 for degrees in the formula: radians = 45 \times \frac{\pi}{180}

Simplify the fraction: \frac{45}{180} = \frac{1}{4}

Multiply the simplified fraction by \pi: \frac{1}{4} \times \pi

Express the final answer as a multiple of \pi: \frac{\pi}{4}

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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, you multiply the degree value by π/180. For example, to convert 45°, you would calculate 45 × (π/180), simplifying to π/4 radians.

Understanding Radians

Radians are a unit of angular measure used in mathematics, particularly in trigonometry. One radian is defined as the angle created when the arc length is equal to the radius of the circle. This unit is more natural for mathematical calculations involving circles and periodic functions compared to degrees.

Simplifying Fractions

When converting degrees to radians, the resulting fraction often needs simplification. This involves reducing the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For instance, in the conversion of 45° to radians, π/4 is already in its simplest form.