# Ch 21: Trigonometric Graphs: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering high school precalculus material will benefit from taking this course. There is no faster or easier way to learn high school precalculus. Among those who would benefit are:

- Students who have fallen behind in understanding trigonometric graphs or working with graphs to determine trigonometric identity.
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about trigonometric graphs
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Trigonometric Graphs chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know, review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Trigonometric Graphs chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any trigonometric graphing question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

In this chapter, you'll learn the answers to questions including:

- What are the steps for graphing sine and cosine transformations?
- What are the steps for graphing tangent function, including amplitude, phase and period?
- How do I to use graphs to find trigonometric identity?
- How can I use graphs to solve trigonometric equations?

### 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. 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.

### 4. Using Graphs to Determine Trigonometric Identity

After watching this video lesson, you will be able to use graphs to determine whether an equation is a trigonometric identity or not. Learn what you need to look for to determine this.

### 5. Solving a Trigonometric Equation Graphically

How can you show someone that you have the right answer? This video lesson will show you how you can do this for a trigonometric equation. Learn what you need to watch for and how to get your answers.

### 6. How to Graph cos(x)

The cosine function shows up often in mathematics, so being familiar with it is very useful. We will learn how to graph cos(x) using its various properties, and we'll look at how to use the graph of the sine function to create the graph of cos(x).

### 7. How to Graph 1-cos(x)

Let's see how to graph 1 - cos(x). We'll do this using transformations of the function cos(x). After graphing 1 - cos(x), let's dig a little deeper into transformations of functions, and see how useful they are in graphing seemingly complex functions.

### 8. 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.

### 9. How to Find the Phase Shift of a Trig Function

As long as your trig function is written in standard form, you can easily find your phase shift. You just need to know which two numbers to look at and how to combine them.

### 10. How to Find the Vertical Shift of a Trig Function

In this how-to lesson, you'll learn how you can find the vertical shift of any trig function easily just by looking at one particular number in the whole function.

### 11. How to Find the Frequency of a Trig Function

In this lesson, we explore how to determine the frequency of trigonometric functions. In addition to the sine function, we will look at cosine, tangent, cotangent, cosecant, and secant.

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### Other Chapters

Other chapters within the High School Precalculus: Help and Review course

- Working with Linear Equations: Help and Review
- Working With Inequalities: Help and Review
- Absolute Value Equations: Help and Review
- Working with Complex Numbers: Help and Review
- Systems of Linear Equations: Help and Review
- Mathematical Modeling: Help and Review
- Introduction to Quadratics: Help and Review
- Working with Quadratic Functions: Help and Review
- Geometry Basics for Precalculus: Help and Review
- Functions - Basics for Precalculus: Help and Review
- Understanding Function Operations: Help and Review
- Graph Symmetry: Help and Review
- Graphing with Functions: Help and Review
- Rate of Change: Help and Review
- Polynomial Functions Basics: Help and Review
- Higher-Degree Polynomial Functions: Help and Review
- Rational Functions & Difference Quotients: Help and Review
- Rational Expressions and Function Graphs: Help and Review
- Exponential Functions & Logarithmic Functions: Help and Review
- Using Trigonometric Functions: Help and Review
- Solving Trigonometric Equations: Help and Review
- Trigonometric Identities: Help and Review
- Trigonometric Applications in Precalculus: Help and Review
- Graphing Piecewise Functions: Help and Review
- Vectors, Matrices and Determinants: Help and Review
- Mathematical Sequences and Series: Help and Review
- Sets in Algebra: Help and Review
- Analytic Geometry and Conic Sections: Help and Review
- Polar Coordinates and Parameterizations: Help and Review
- Continuity: Help and Review
- Limits: Help and Review