In the preceding chapters, you explore sine and cosine as numeric values based on the lengths of the sides of a right triangle. However, this does not provide a holistic picture of the trigonometric functions themselves. Graphing the functions and transforming those graphs are visually effective ways to better understand sine and cosine as periodic functions.
The graphs of cosine and sine are “periodic,” which means that they repeat over and over as you travel horizontally across the graph. More specifically, they look like waves that wiggle above and below the x-axis to a maximum height of y = 1 and a minimum height of y = –1.
In this chapter, you graph sine and cosine, but you don’t stop there. You also find out what happens to the graphs when you tweak them a little. For example, once you know what the graph of sin x looks like, you’ll be able to quickly sketch the graphs of 3 · sin x and sin 2x.
However, before you even think about sine and cosine, it’s worth spending some time with less complicated periodic graphs to see how they work.