# Graphing Sine/Cosine with Translations

- Author:
- Brian Sterr

- Topic:
- Cosine, Sine, Translation

Use the sliders to adjust the values of , , , and . The first checkbox switches between a sine and a cosine graph. Click the other checkboxes in order to see the steps for graphing a function like this.

The easiest way to graph a sine or cosine function with transformations is to figure out what happens to the period where for the basic function ( or ) after the transformations have been applied.
For a sine function, we can find where ends up. For a cosine function, we look for where gets moved to after the transformations.

- Start by plotting the midline:
- Now go left or right along the midline using the phase shift to get start of the period. For a sine curve, you'll start here at
, while for a cosine curve, you need to take the amplitude into account and you will start at . This will be the start of the period - From here, go right one period to find the end of the period.
- Dividing the period into quarters, we can get the 5 key points for the period (relative minimum, relative maximum, and midline crossings).
- Finally Sketch the curve. It should be smooth.