# Ch 15: Trigonometric Functions

### About This Chapter

## Trigonometric Functions - Chapter Summary

This chapter is designed to provide you with an easy-to-understand introduction to trigonometric functions, including how they can be used to solve real life, mathematical problems. At the beginning of the chapter, the instructor will discuss odd and even trigonometric functions and show you how to create graphs for sine, cosine and tangent functions. You'll also learn about the relationship between trigonometric functions and amplitude and periodicity.

As the chapter continues, the instructor will explain the addition and subtraction formulas for sine, cosine and tangent. Additional topics include a discussion of the Pythagorean Identity. At the end of the chapter, you should be able to:

- Identify and express numerical, written and other representations of trigonometric functions and their inverses
- Recognize and apply connections among trigonometric properties, including axes of symmetry, local extrema and zeroes
- Identify the amplitude, frequency, phase shift and other characteristics of trigonometric functions, graphs of functions and mathematical notations
- Understand the relationships between trigonometric functions and their inverses and use the relationships to solve problems
- Uses trigonometric identities to simplify expressions and solve equations.

Our concise, engaging video lessons on trigonometric functions are intended to help shorten the learning curve for this complex mathematical subject. Taught by experienced, professional instructors, each tutorial is accompanied by a lesson transcript with links to text-based materials and further information. At the end of each chapter, you can use the online self-assessments to find out how well you understood the presentation. If you need to review a key term or concept, the video tags allow you to locate specific parts of the video, without having to re-watch the entire lesson.

### 1. Trigonometric Functions: Definition & Examples

In mathematics, trigonometric functions are functions of angles. This lesson will describe the 6 main trigonometric functions, use them to solve problems, and give some examples. The quiz at the end of the lesson will allow you to practice what you've learned.

### 2. How to Graph Trigonometric Functions

In this lesson, you'll learn how to read a trigonometric function so that you could recognize it on a graph. There isn't much math to it, you just have to know which numbers to look at.

### 3. Even & Odd Functions: Definition & Examples

Even and odd functions are an aspect of line symmetry. You can use knowledge of even and odd functions to quickly identify equation symmetry. After this lesson, test your knowledge with a short quiz!

### 4. How to Find the Period of a Trig Function

Read this lesson to learn how you can find the period of any trig function you are given. You'll see how the period changes when dealing with cosine and sine functions versus tangent and cotangent functions.

### 5. How to Find Amplitude of a Sine Function

In this lesson we look at a method for finding the amplitude of a sine function. This method works even when the equilibrium line is not the horizontal axis.

### 6. 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.

### 7. Inverse Trigonometric Functions: Definition & Problems

In mathematics, an inverse operation can reverse the effect of another operation. This lesson explains how inverse trigonometric functions work and provides examples of how they are used in scientific fields and real-life situations.

### 8. Domain & Range of Trigonometric Functions & Their Inverses

In mathematics, every function has a particular domain and range. In this lesson, we will learn about the domains and ranges of the trigonometric functions and their inverses.

### 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. How to Solve Trigonometric Equations: Practice Problems

Trig equations can look like some kind of alien language, but once you get the principles down, they're not too bad. In this lesson, we'll work through some examples.

### 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.

### 12. Pythagorean Identities: Uses & Applications

After watching this video lesson, you will be able to spot the Pythagorean identities when you see them. You will also learn how these identities can help you solve more complicated trig problems.

### 13. Proving the Addition & Subtraction Formulas for Sine, Cosine & Tangent

Watch this video lesson, and you will see how the angle sum and difference identities are derived for sine, cosine, and tangent. You will also learn how you can use these identities to help you solve problems.

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### Other Chapters

Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course

- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Triangles
- Circles
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards