Using Transformations to Graph Trig Functions (5 Examples) [Video]

In this video, I discuss the six basic trigonometric functions and their graphs. I cover transformations such as a change in period, phase shift, amplitude, and vertical and horizontal shifts. I work on five examples in detail.

In this video, I’m going to talk about the graphs of sines and cosines. We will discuss various ways to transform them and get more complex graphs, starting from knowing what a basic sine graph looks like and a basic cosine graph. And then we will be able to do transformations. For example, we will change the period, change the phase shift, and make vertical and horizontal shifts. So in this video, I will work on 5 precalculus problems using transformations to graph trig functions.

Using Transformations to Graph Trig Functions FAQ

How do you translate trigonometric functions? You can translate a function either using a vertical shift (shifting function up or down) or using a horizontal shift left or right. 

What is the period of a function? Every periodic function has a period. If a function has a graph composed of repeated cycles, then the period is the horizontal distance of one cycle. 

How do you graph sine and cosines without a calculator? The first step is knowing the basic six trigonometric functions. Then the second step is understanding the periods of these six functions and how the period can change. The third step is to understand the phase shift and amplitude and how they can change. After that, knowing how translations can occur. From these basic transformations (and the shapes of the basic six trigonometric functions), you can graph a wide variety of trigonometric functions.

How do you memorize trig graphs? The idea is to remember the basic six trigonometric graphs and then learn how to apply transformations. In practicing this skill, remember to sketch the graph of the basic underlying function. This repetition will help you remember it for future use. 

See related videos here in the Precalculus Problems playlist on YouTube.

If you would like to have your own problems solved using transformations to graph trig functions make a request here.

About David A. Smith aka Dave
About Dave

David Smith (Dave) has a B.S. and M.S. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. David is the founder and CEO of Dave4Math.

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