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

2. 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.

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

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

5. 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.

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

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

8. Example 3: Horizontal Stretching
Sketch the graph of

9. Example 4: Horizontal Translation
Analyze the graph of

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

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

12. 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?

13. Homework
Pg 330 #1-65 ODD