# Ch 11: Explorations in Core Math Algebra 2 Chapter 11: Trigonometric Graphs and Identities

### About This Chapter

## Explorations in Core Math Algebra 2 Chapter 11: Trigonometric Graphs and Identities - Chapter Summary and Learning Objectives

This chapter will help you analyze trigonometric graphs and identities. Lessons will explain how to graph a number of trigonometric functions and guide you to an understanding of various identities. You can focus on increasing what you know about:

- Graphs of the sine, cosine and tangent
- How to graph the cosecant, secant and cotangent
- Trigonometric, double-angle and half-angle identities
- Sum and difference identities
- Unit circles
- Trigonometric equations

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

Graphing Sine and Cosine | Evaluate how sine and cosine can be graphed on a unit circle. |

Graphing Sine and Cosine Transformations | Calculate what happens to sine and cosine waves when they're transformed. |

Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift | Assess how tangent functions can be graphed and transformed. |

Graphing the Cosecant, Secant & Cotangent Functions | Develop the ability to identify graphs of the cosecant, secant and cotangent with and without transformations. |

Trigonometric Identities: Definition & Uses | Consider and recognize different identities. |

Verifying Trigonometric Identities with Unit Circles | Focus on using the unit circle to validate trigonometric identities. |

Applying the Sum & Difference Identities | Compare the six sum and difference identities. |

Double-Angle Identities: Uses & Applications | Negotiate the usage of double-angle identities in trigonometry. |

Half-Angle Identities: Uses & Applications | Explain how to use half-angle identities to simplify trigonometry problems. |

Writing & Revising Trigonometric Equations | Develop your ability to write and revise trigonometric equations. |

### 1. Graphing Sine and Cosine

Sine and cosine aren't just for triangles; they can also be waves. See them graphed on the unit circle and then learn how that translates into the sine and cosine waves.

### 2. Graphing Sine and Cosine Transformations

What happens when we take the sine and cosine wave and transform them? They get bigger, smaller, faster and slower. Find out how in this lesson on sine and cosine wave transformations.

### 3. Graphing the Tangent Function: Amplitude, Period, Phase Shift & Vertical Shift

Take a look at how the graph of a tangent function and how we can transform it by making a few small changes to its equation. This video shows how to graph the original function and explains its transformations.

### 4. Graphing the Cosecant, Secant & Cotangent Functions

After watching this video lesson, you will learn what the graphs of the cosecant, secant, and cotangent trigonometric functions look like. You will also learn how to see if these graphs are shifted or transformed.

### 5. Trigonometric Identities: Definition & Uses

After watching this video lesson, you will understand what a trigonometric identity is. You will also know the different kinds of identities you will come across.

### 6. Verifying Trigonometric Identities with Unit Circles

In this lesson, we will review the unit circle and the corresponding definitions of the trigonometric functions. We will then verify several trigonometric identities using the unit circle.

### 7. Applying the Sum & Difference Identities

Watch this video lesson to learn the six sum and difference identities for the trig functions of sine, cosine, and tangent. Also, learn how you can use them to your advantage when solving tough trig problems.

### 8. Double-Angle Identities: Uses & Applications

Watch this video lesson to learn how you can use the double-angle identities in trigonometry to help you prove and solve more complicated trigonometry problems.

### 9. Half-Angle Identities: Uses & Applications

After watching this video lesson, you will be able to use half-angle identities to help you simplify your trig problems and also to help you prove other trig statements.

### 10. Writing & Revising Trigonometric Equations

Read this lesson to learn how you can write a trigonometric equation for the Ferris wheel problem and then rewrite it to find the height of a rider as the Ferris wheel spins around.

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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 10: Trigonometric Functions
- Explorations in Core Math Algebra 2 Chapter 12: Conic Sections