# Ch 11: Trigonometry: College Precalculus Lesson Plans

### About This Chapter

## Weekly Syllabus

Below is a sample breakdown of the Trigonometry chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day | Topics | Key Terms and Concepts Covered |
---|---|---|

Monday | Basic trigonometric functions | Graphs of sine, cosine and tangent; period, amplitude and phase shift transformations |

Tuesday | The unit circle | Degree and radian measures for the first quadrant of the unit circle; trigonometric properties of right triangles |

Wednesday | The law of sines and the law of cosines | Methods for using the law of sines and the law of cosines to find missing sides and angles of triangles |

Thursday | Applications of trigonometric functions | Procedures for applying the double angle formula, converting between radians and degrees and solving trigonometric equations |

Friday | Trigonometric identities | Connections between the Pythagorean theorem and the basic trigonometric identities |

### 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. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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 College Precalculus Syllabus Resource & Lesson Plans course

- Functions: College Precalculus Lesson Plans
- Exponential & Logarithmic Functions: College Precalculus Lesson Plans
- Inequalities: College Precalculus Lesson Plans
- Foundations & Linear Equations: College Precalculus Lesson Plans
- Graphing & Rational Equations: College Precalculus Lesson Plans
- Quadratic Equations: College Precalculus Lesson Plans
- Exponents & Polynomials: College Precalculus Lesson Plans
- Piecewise & Composite Functions: College Precalculus Lesson Plans
- Geometry & Trigonometry: College Precalculus Lesson Plans
- Using Scientific Calculators: College Precalculus Lesson Plans