# Ch 22: Algebra II: Trigonometry

### About This Chapter

## Algebra II: Trigonometry - Chapter Summary and Learning Objectives

This chapter dives quickly into several trigonometry topics. You'll start by learning how to graph sine and cosine transformations, as well as tangent functions. Lessons provide overviews of different types of special triangles. You'll also develop the mathematical skills needed to solve trigonometric equations. At the end of this chapter, you should have a strong understanding of the following topics:

- Sine and cosine transformations
- Unit circles
- Special right triangles
- The double angle formula
- Radian and degree conversions
- Basic trigonometric identities

Video | Objective |
---|---|

Graphing Sine and Cosine Transformations | Be able to graph sine and cosine unit circles and transformations. |

Graphing the Tangent Function: Amplitude, Period, Phase Shift and Vertical Shift | Understand how to graph the tangent function and explain shifts of A/B/lambda. |

Unit Circle: Memorizing the First Quadrant | Memorize and name the first quadrant of the unit circle, including x- and y-values of 0, 30, 45, 60 and 90 degree angles. |

Using Unit Circles to Relate Right Triangles to Sine and Cosine | Relate right triangles to the sine and cosine using unit circles. |

Special Right Triangles: Types and Properties | List the common properties of special right triangles, including 45-45-90 triangles and 30-60-90 triangles. |

Law of Sines: Definition and Application | Understand the law of sines and how to use two angles and a side to define the entire triangle. |

Law of Cosines: Definition and Application | Define the law of cosines and apply the law to finding triangle angles. |

The Double Angle Formula | Apply the angle sum formula to a double angle. |

Converting Between Radians and Degrees | Convert angles in radians to degrees and vice versa. |

How to Solve Trigonometric Equations for X | Correctly solve trigonometric equations for x. |

List of the Basic Trig Identities | Name the basic trigonometric identities and corresponding angles. |

### 1. 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.

### 2. 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.

### 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. Special Right Triangles: Types and Properties

Not all right triangles are the same. In this lesson, we'll look at two special right triangles (30-60-90 and 45-45-90) that have unique properties to help you quickly and easily solve certain triangle problems.

### 6. 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.

### 7. 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.

### 8. The Double Angle Formula

When you encounter a doubled angle, there are special formulas that can help you handle trigonometric value. In this lesson, we'll define and practice using the double angle formulas for sine, cosine and tangent.

### 9. Converting Between Radians and Degrees

Angles can be measured in degrees or radians. This lesson will explore the difference and provide you with a simple calculation that can be used to convert degrees into radians and radians into degrees.

### 10. How to Solve Trigonometric Equations for X

Adding trigonometric functions into standard algebra equations adds complexity. Learn how to solve trigonometric equations for x and how to use inverse operations to simplify equations.

### 11. List of the Basic Trig Identities

There are specific trig functions that have very special and very simple relationships with each other. Learn the main one and how you can use it to understand the others.

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### Other Chapters

Other chapters within the Algebra II: High School course

- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Homeschool Resources for High School Algebra II