Use the sliders to adjust the values of [math]a[/math], [math]b[/math], [math]c[/math], and [math]d[/math]. 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 [math]x\in\left[0,2\pi\right][/math] for the basic function ([math]y=\sin x[/math] or [math]y=\cos x[/math]) after the transformations have been applied.[br]For a sine function, we can find where [math]\left(0,0\right)[/math] ends up. For a cosine function, we look for where [math]\left(0,1\right)[/math] gets moved to after the transformations.[br][list=1][*]Start by plotting the midline: [math]y=d[/math][br][/*][*]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 [math]\left(c,d\right)[/math], while for a cosine curve, you need to take the amplitude into account and you will start at [math]\left(c,a+d\right)[/math]. 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.[/*][/list]