# Ch 10: Explorations in Core Math Algebra 2 Chapter 10: Trigonometric Functions

### About This Chapter

## Explorations in Core Math Algebra 2 Chapter 10: Trigonometric Functions - Chapter Summary and Learning Objectives

Strengthen your comprehension and skill in working with trigonometric functions, applying the laws of sines and cosines and measuring angle of rotation using the lessons in this chapter. Our instructors are available for assistance if you need it, and the dashboard allows you to track your work and stay organized. The lessons cover the material shown below and more:

- Formula and explanation of radian measure
- Applications of the laws of sines and cosines
- Techniques for memorizing the unit circle
- How to identify special angles and inverse trigonometric functions

Lesson | Objective |
---|---|

Radian Measure: Definition & Formula | Use the formula for radian measure. |

Angle of Rotation: Definition & Measurement | Measure and define angle of rotation. |

Unit Circle: Memorizing the First Quadrant | Commit unit circle to memory. |

Using Unit Circles to Relate Right Triangles to Sine & Cosine | Use unit circle to connect sine and cosine to right triangles. |

Practice Problems with Circular Trigonometric Functions | Solve trig problems using unit circle. |

Identifying Reference Angles: Process & Examples | Demonstrate procedure for identifying reference angles. |

Trigonometric Function Values of Special Angles | Identify special angles and corresponding trig values. |

Properties of Inverse Trigonometric Functions | Understand the notation and characteristics of inverse trig functions. |

Solve Trigonometric Equations with Identities & Inverses | Use identities and inverses to find solutions to trigonometric equations. |

Law of Sines: Definition and Application | Explain and apply the law of sines. |

Using the Law of Sines to Solve a Triangle | Solve a triangle with the law of sines. |

Law of Cosines: Definition and Application | Examine the applications of the law of cosines. |

Solving Real World Problems Using the Law of Cosines | Apply the law of cosines to everyday problems. |

### 1. Radian Measure: Definition & Formula

In mathematics, the radian is the standard unit of angular measure. This lesson will define radian and work through some problems involving radians. The lesson will end with a quiz.

### 2. Angle of Rotation: Definition & Measurement

In this lesson we describe angles of rotation using four different measures. We will use these ideas to define and draw angles while suggesting how this skill could be used as a game.

### 3. Unit Circle: Memorizing the First Quadrant

Memorizing the unit circle can be a daunting task, but this lesson will show you a pattern to help you memorize the points, degree measures, and radian measures for the entire first quadrant.

### 4. Using Unit Circles to Relate Right Triangles to Sine & Cosine

The unit circle is a helpful tool for understanding trigonometric concepts. In this lesson, we'll look at right triangles on the unit circle to better grasp sine and cosine.

### 5. Practice Problems with Circular Trigonometric Functions

After watching this video lesson, you will be able to use the unit circle to help you find your answer to trig problems without making too many calculations. Watch and learn how you can find your angle in radians on the unit circle.

### 6. Identifying Reference Angles: Process & Examples

This lesson will explain how to identify reference angles in the coordinate plane. It will also provide multiple examples of how to find reference angles in the coordinate plane.

### 7. Trigonometric Function Values of Special Angles

After watching this video lesson, you will better understand the six trigonometric functions. You will also know what special angles there are and what the trigonometric values for these special angles are.

### 8. Properties of Inverse Trigonometric Functions

After watching this video lesson, you will understand why our inverse trigonometric functions have a limited range. Learn what this does. Also learn the notation for these functions.

### 9. Solve Trigonometric Equations with Identities & Inverses

After watching this video lesson, you will be able to solve trigonometric equations by making use of trigonometric identities and inverses. Learn the steps to take to get to your solution.

### 10. Law of Sines: Definition and Application

Don't get stuck trying to find missing sides or angles in a triangle. Use the Law of Sines to rescue you from any perilous triangle in which you have just a few pieces of information.

### 11. Using the Law of Sines to Solve a Triangle

After watching this video lesson, you will be able to use the law of sines to find a missing side of a triangle as well as a missing angle of a triangle. Learn what you need to know about the triangle in order to use the formula.

### 12. Law of Cosines: Definition and Application

In this lesson, we'll learn how to solve problems involving three sides and one angle in a triangle. The Law of Cosines, a modification of the Pythagorean Theorem, will save the day.

### 13. Solving Real World Problems Using the Law of Cosines

After watching this video lesson, you will be able to use the law of cosines to solve real-world problems. Learn what kinds of real-world problems the law of cosines can help you solve.

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### Other Chapters

Other chapters within the Explorations in Core Math - Algebra 2: Online Textbook Help course

- Explorations in Core Math Algebra 2 Chapter 1: Foundations for Functions
- Explorations in Core Math Algebra 2 Chapter 2: Quadratic Functions
- Explorations in Core Math Algebra 2 Chapter 3: Polynomial Functions
- Explorations in Core Math Algebra 2 Chapter 4: Exponential and Logarithmic Functions
- Explorations in Core Math Algebra 2 Chapter 5: Rational and Radical Functions
- Explorations in Core Math Algebra 2 Chapter 6: Properties and Attributes of Functions
- Explorations in Core Math Algebra 2 Chapter 7: Probability
- Explorations in Core Math Algebra 2 Chapter 8: Data Analysis and Statistics
- Explorations in Core Math Algebra 2 Chapter 9: Sequences and Series
- Explorations in Core Math Algebra 2 Chapter 11: Trigonometric Graphs and Identities
- Explorations in Core Math Algebra 2 Chapter 12: Conic Sections