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

Radians

Trigonometry

1. Measuring Angles

Radians

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2: minutes

Problem 14

Textbook Question

In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.18°

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 angle in degrees into the formula: \( 18° \times \frac{\pi}{180} \).

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.

The simplified fraction will give you the angle in radians as a multiple of \( \pi \).

Express the final result as a simplified fraction multiplied by \( \pi \).

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Key Concepts

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

Degrees and Radians

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 to the other.

Conversion Formula

To convert an angle from degrees to radians, you can use the formula: radians = degrees × (π/180). This formula allows you to express the angle in radians as a multiple of π, which is often required in trigonometric contexts.

Multiples of π

Expressing angles in terms of multiples of π is common in trigonometry. For example, an angle of 18° converted to radians would be expressed as a fraction of π, making it easier to work with in equations and functions that involve trigonometric ratios.