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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2:27 minutes

Problem 20

Textbook Question

In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.-270°

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: \(-270° \times \frac{\pi}{180} \).

Simplify the fraction: \(-270 \div 180 = -\frac{3}{2} \).

Multiply the simplified fraction by \(\pi\): \(-\frac{3}{2} \pi\).

Express the angle in radians as a multiple of \(\pi\): \(-\frac{3}{2} \pi\).

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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. To convert between these units, the relationship can be used: 180 degrees equals π radians. Understanding this conversion is essential for solving problems involving angle measurements.

Conversion Formula

The conversion from degrees to radians can be achieved using the formula: radians = degrees × (π/180). This formula allows for the straightforward transformation of angle measurements, making it easier to work with trigonometric functions that often use radians as their standard unit.

Negative Angles

Negative angles indicate a clockwise rotation from the positive x-axis. For example, -270° represents a rotation of 270 degrees in the clockwise direction. Understanding how to interpret negative angles is crucial for accurately converting and visualizing angles in both degrees and radians.