Section 1.5 Graphs of Sine and Cosine Functions

Section Objectives

  1. Sketch the graphs of general sine and cosine functions.


Basic Graphs

Before we even start sketching the graphs of and , we should recall a few important ideas about these functions.



The graph of is shown here.

 

 




The graph of is shown here.




More General Graphs

Look carefully for the key ideas that were outlined above. By thinking about how those ideas change under transformations, we can easily graph the general sine and cosine functions:



Examples










Period, Amplitude, and Phase Shifts

The graphs of and have the following characteristics (assuming ):



As a general rule of thumb, we can sketch the graphs of more general sine and cosine functions by using this procedure:

  1. Sketch the graph of the corresponding basic function without the axes scaled.
  2. Scale the axes to satisfy the characteristics described above.
  3. Redraw, if necessary, to make a "cleaner" graph.


It is sometimes useful to write

or



Examples