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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1:56 minutes

Problem 23

Textbook Question

In Exercises 21–28, convert each angle in radians to degrees.2𝜋3

Verified step by step guidance

Recall the conversion factor between radians and degrees: 1 radian = \( \frac{180}{\pi} \) degrees.

Multiply the given angle in radians by the conversion factor to convert it to degrees.

For the angle \( \frac{2\pi}{3} \), multiply by \( \frac{180}{\pi} \) to convert to degrees: \( \frac{2\pi}{3} \times \frac{180}{\pi} \).

Simplify the expression by canceling out \( \pi \) from the numerator and the denominator.

Calculate the resulting expression to find the angle in degrees.

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Key Concepts

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

Radians and Degrees

Radians and degrees are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. To convert between these units, one can use the relationship that 180 degrees equals π radians, allowing for straightforward calculations.

Conversion Formula

The conversion from radians to degrees can be performed using the formula: degrees = radians × (180/π). This formula provides a direct method to translate the measure of an angle from radians to degrees, ensuring accurate results in various applications.

Understanding π

The constant π (pi) is approximately 3.14159 and represents the ratio of a circle's circumference to its diameter. In trigonometry, π is crucial for defining the relationship between radians and degrees, as it appears in the conversion formulas and helps in understanding circular motion and periodic functions.