About This Chapter
Trigonometric Graphs - Chapter Summary
As you develop a better understanding of trigonometric functions, you will start to recognize the methods used for shifting, stretching, and shrinking trigonometric graphs. These lessons identify all of the major trigonometric graphing procedures, and they also point out the trigonometry vocabulary words you will need to understand. Each brief lesson within the chapter focuses on one major topic at a time. You can review the lessons in order, or you can skip around, depending on your study needs. Our instructors provide ample illustrations and sample problems to help you verify trigonometric identities and solve trigonometric equations. This chapter is designed to teach you how to:
- Describe graphing cosine and sine transformations
- Identify vertical shift, phase shift, period, and amplitude
- Analyze graphing cotangent, secant, and cosecant functions
- Define the trigonometric identity through using graphs
- Examine how to 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. 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).
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. 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.
5. 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.
6. 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.
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Other chapters within the Precalculus: High School course
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Teacher Resources for Precalculus in High School