Graphs of Sine and Cosine Functions Section 4.5 Graphs of Sine and Cosine Functions

Objective By following instructions students will be able to: Sketch the graphs of basic sine and cosine functions. Use amplitude and period to help sketch the graphs of sine and cosine functions. Sketch translations of graphs of sine and cosine functions.

Sine Graph y=asin(bx-c)+d intercepts maximum minimum period = one cycle

Cosine Graph y=a cos(bx-c)+d period = one cycle intercepts maximum minimum

Amplitude and Period of Sine and Cosine Curves If a>1 , vertical stretch. If -1<a<1, vertical shrink. The range of the amplitude is . Period Left and Right Endpoints Left Endpoint Right Endpoint Vertical Translation If d>1, graph shifts d units up. If d<1, shifts d units down.

Example 1: Using Key Points to Sketch a Sine Curve Sketch the graph of On the interval of .

Example 2: Vertical Shrinking and Stretching On the same coordinate axes, sketch the graph of each function. a) b) c)

Example 3: Horizontal Stretching Sketch the graph of .

Example 4: Horizontal Translation Analyze the graph of .

Example 5: Horizontal Translation Use a graphing utility to analyze the graph of

Example 6: Vertical Translation Use a graphing utility to analyze the graph of

Revisit Objective Did we… Sketch the graphs of basic sine and cosine functions? Use amplitude and period to help sketch the graphs of sine and cosine functions? Sketch translations of graphs of sine and cosine functions?

Homework Pg 330 #1-65 ODD