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

by Dave
(DAVE)—

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.

Let’s face it; plotting points is boring. That’s why, in this video, I’m going to talk to you about using transformations to graph trig functions. Starting from basic graphs, I will discuss various ways to transform the graphs of sines and cosines so that you can sketch more complex graphs.

Hi everyone, I’m Dave. In this episode, I share with you five precalculus problems that use transformations to graph trigonometric functions. For example, I will change the period, change the phase shift, and make vertical and horizontal shifts.

## Examples Using Transformations to Graph Trig Functions

1. Sketch the graph of the function $y=2+\frac{1}{10} \cos 60\pi x$ and include two full periods.
2. Sketch the graph of the function $y=3\cos(x+\pi)-3$ and include two full periods.
3. Sketch the graph of the function $y=\frac{2}{3}\cos\left(\frac{x}{2}-\frac{\pi}{4}\right)$ and include two full periods.
4. The function $g(x)=\cos(x-\pi)+2$ is related to a parent function $f(x)=\sin x$ or $f(x)=\cos x$. (a) Describe the sequence of transformations from $f$ to $g$. (b) Sketch the graph of $g$. (c) Use function notation to write $g$ in terms of $f$.
5. The function $g(x)=2\sin(4x-\pi)-3$ is related to a parent function $f(x)=\sin x$ or $f(x)=\cos x$. (a) Describe the sequence of transformations from $f$ to $g$. (b) Sketch the graph of $g$. (c) Use function notation to write $g$ in terms of $f$.

## Conclusion

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.