# 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 $f$.