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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2:11 minutes

Problem 18

Textbook Question

In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.330°

Verified step by step guidance

Understand the relationship between degrees and radians: 180° is equivalent to \( \pi \) radians.

To convert degrees to radians, use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).

Substitute 330° into the formula: \( 330° \times \frac{\pi}{180} \).

Simplify the fraction \( \frac{330}{180} \) by finding the greatest common divisor of 330 and 180.

Express the simplified fraction as a multiple of \( \pi \).

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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 terms of π, which is often required in trigonometric contexts.

Multiples of π

When expressing angles in radians, it is common to represent them as multiples of π. For example, an angle of π/6 radians corresponds to 30 degrees. This representation simplifies calculations in trigonometry and helps in understanding the properties of angles.