# Ch 17: Trigonometric Functions & Graphs Review

### About This Chapter

## Trigonometric Functions & Graphs Review - Chapter Summary

High school students need to read and understand a great deal of information both before they graduate and as they move on in college or the professional world. This chapter provides students with focused training on reviewing essential knowledge of trigonometric functions and graphs

Instead of an endless chapter of information, the chapter has been divided into short, individualized lessons. Students have the option to review all of the lessons in order, but they can also pick and choose lesson topics in which they need the most assistance. The chapter menu provides a list of all lessons available, and since each lesson is only focused on a single topic, students can easily find what they need. After completing this chapter, students will be ready to:

- Explain what sine and cosine are
- Memorize the first quadrant of the unit circle
- Use the unit circle to relate right triangles to sine and cosine
- Understand types and properties of special right triangles
- Define the law of sines and apply it to trigonometric problems
- Define the law of cosines and apply it to trigonometric problems
- Understand and use the double angle formula
- Convert measures from radians to degrees
- Graph sine and cosine transformations
- Graph the tangent function

### 1. Trigonometry: Sine and Cosine

Sine and cosine are basic trigonometric functions that are used to solve for the angles and sides of triangles. Review trigonometry concepts and learn about the mnemonic used for sine, cosine, and tangent functions.

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

Memorizing the unit circle allows for calculation of its angles' trigonometric values without a calculator. Explore and memorize the unit circle's first quadrant, including its main points, and its sine, cosine, and tangent values.

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

A unit circle is a circle with a radius of 1, and a right triangle is a triangle with one right angle. Learn the trigonometric properties of right triangles and how to use unit circles to relate right triangles to sine and cosine.

### 4. Special Right Triangles: Types and Properties

There are two types of special right triangles that have either 30-60-90 degree angles or 45-45-90 degree angles. Learn more about the definitions and explore the properties of 30-60-90 and 45-45-90 degree angles of special right triangles through examples.

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

Law of Sines, also known as sine law or sine rule, is an equation relating the sines of the three angles of a triangle to its three sides. Learn about the definition of the Law of Sines and understand how to apply it by completing math problems involving triangles.

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

The law of cosines is an equation that considers the two known sides of a triangle and the cosine of one of its known angles to find the one missing side. Explore the definition and application of the law of cosines and learn how to solve problems involving triangles through the given practice problems.

### 7. The Double Angle Formula

In trigonometry, a double angle is twice as large as a common angle. Learn how to calculate the double angle formula, explore trigonometry twins for sine, cosine, and tangent, and apply this information in practice problems using the double angle formula.

### 8. Converting Between Radians and Degrees

The two most widely used units of measure for angles are degrees and radians. Learn how to convert radians to degrees and degrees to radians using the concepts of proportion and priority.

### 9. Graphing Sine and Cosine Transformations

The sine and cosine signal waveforms, or waves, can be transformed in multiple ways. Learn how to identify the three types of sine and cosine transformations, including amplitude, period, and phase shift, and practice graphing the transformations with sample problems.

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

Unlike other trigonometric functions, a tangent function can be transformed in four different ways. Learn how to graph the tangent function and to visualize and change the amplitude, period, phase shift, and vertical shift of a tangent function.

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### Other Chapters

Other chapters within the High School Precalculus: Homeschool Curriculum course

- Graphing with Functions Review
- Working With Inequalities Review
- Absolute Value Equations Review
- Working with Complex Numbers Review
- Quadratic Functions Review
- Solving & Graphing Quadratic Functions
- Polynomial Functions Review
- Working with Polynomial Functions
- Graphing Piecewise Functions
- Graph Symmetry
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions & Equations Review
- Graphing Rational Functions
- Exponential & Logarithmic Functions Review
- Working with Exponential & Logarithmic Functions
- Solving Trigonometric Identities
- Trigonometric Graphs & Applications
- Understanding Vectors, Matrices & Determinants
- Working with Matrices & Determinants
- Mathematical Sequences & Series Review
- Sets in Algebra
- Analytic Geometry & Conic Sections Review
- Polar Coordinates and Parameterizations
- Continuity
- Limits
- Precalculus: Homeschool Assignments & Projects
- Homeschool Resources for Precalculus in High School