Google Classroom
GeoGebraGeoGebra Classroom

Graphing Sine/Cosine with Translations

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.
  1. Start by plotting the midline:
  2. 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
  3. From here, go right one period to find the end of the period.
  4. Dividing the period into quarters, we can get the 5 key points for the period (relative minimum, relative maximum, and midline crossings).
  5. Finally Sketch the curve. It should be smooth.