The Graphs of sin x and cos x

We are now in a position to graph sin x and cos x. Literally connecting the dots from a few key values of the functions (from our table above) yields the following:

These graphs show one period of the function or one cycle of the graph of each function. From the first remark in the previous section, we can extend these graphs infinitely in both directions to obtain the following:

Note also, as we commented in the previous section, that the y-values stay between -1 and 1.

Given these graphs, you can probably imagine how these functions could be used to model many different real-world phenomena. We will talk about such examples later in our text.

Several natural questions arise now in terms of these graphs. How can we make the period smaller or larger (in essence, to ``stretch'' or ``shrink'' the graph in the horizontal direction)? How can I move the graph up or down? How can I ``stretch'' the graph up, so that the y-values range from [-5, 5], for example?