Table of contents

0. Review of College Algebra4h 45m

Rationalizing Denominators
17m

Pythagorean Theorem & Basics of Triangles
17m

Basics of Graphing
30m

Functions
41m

Transformations
45m

Asymptotes
4m

Solving Linear Equations
31m

Solving Quadratic Equations
55m

Complex Numbers
41m

1. Measuring Angles40m

Angles in Standard Position
12m

Coterminal Angles
8m

Complementary and Supplementary Angles
10m

Radians
8m

2. Trigonometric Functions on Right Triangles2h 5m

Trigonometric Functions on Right Triangles
45m

Special Right Triangles
30m

Cofunctions of Complementary Angles
26m

Solving Right Triangles
23m

3. Unit Circle1h 19m

Defining the Unit Circle
14m

Trigonometric Functions on the Unit Circle
9m

Common Values of Sine, Cosine, & Tangent
11m

Reference Angles
38m

Reciprocal Trigonometric Functions on the Unit Circle
6m

4. Graphing Trigonometric Functions1h 19m

Graphs of the Sine and Cosine Functions
32m

Phase Shifts
14m

Graphs of Secant and Cosecant Functions
10m

Graphs of Tangent and Cotangent Functions
21m

5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m

Inverse Sine, Cosine, & Tangent
28m

Evaluate Composite Trig Functions
44m

Linear Trigonometric Equations
28m

6. Trigonometric Identities and More Equations2h 34m

Introduction to Trigonometric Identities
1h 4m

Sum and Difference Identities
1h 3m

Double Angle Identities
16m

Solving Trigonometric Equations Using Identities
9m

7. Non-Right Triangles1h 38m

Law of Sines
49m

Law of Cosines
30m

Area of SAS & ASA Triangles
19m

8. Vectors2h 25m

Geometric Vectors
28m

Vectors in Component Form
32m

Direction of a Vector
23m

Unit Vectors and i & j Notation
27m

Dot Product
22m

Cross Product
11m

9. Polar Equations2h 5m

Polar Coordinate System
29m

Convert Points Between Polar and Rectangular Coordinates
26m

Convert Equations Between Polar and Rectangular Forms
29m

Graphing Other Common Polar Equations
39m

10. Parametric Equations1h 6m

Graphing Parametric Equations
12m

Eliminate the Parameter
32m

Writing Parametric Equations
21m

11. Graphing Complex Numbers1h 7m

Graphing Complex Numbers
6m

Polar Form of Complex Numbers
22m

Products and Quotients of Complex Numbers
14m

Powers of Complex Numbers (DeMoivre's Theorem)
23m

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.