1. Period and Amplitude Changes
8.2 Sine and Cosine Curves
Period and Amplitude Changes

2. 8.2 Sine and Cosine Curves Objectives: Vocabulary:
Evaluate sine and cosine functions with amplitude and period changes
Vocabulary:
Amplitude, period

3. Graph of the Sine Function
To sketch the graph of y = sin x first locate the key points. These are the maximum points, the minimum points, and the intercepts. -1 1
sin x x
Then, connect the points on the graph with a smooth curve that extends in both directions beyond the five points. A single cycle is called a period. y x
y = sin x
Remember that y = sin x is an odd function whose graph is symmetry to origin.

4. Transformations of Trig Functions
Amplitude |A|: A controls vertical stretching/shrinking
Period p can be in radians or degrees: p is the horizontal length to complete one cycle
B can be in radians or degrees: B controls horizontal stretching/shrinking

5. SINE FUNCTION
Period =2π
Amplitude = 1

6. COSINE FUNCTION
Period =2π
Amplitude = 1

7. Vertical Stretching/Shrinking of Sine Functions
KEY TAKE-AWAY: x-intercepts are unchanged; multiply y-value of max/min by A.

8. y = sin(x)
y = sin(2x)

9. y = sin(x)
y = sin(x/2)

12. Sketch the graph of y = sin (–x).
The graph of y = sin (–x) is the graph of y = sin x reflected in the x-axis. y x
y = sin (–x)
y = sin x
Sketch the graph of y = cos (–x).
The graph of y = cos (–x) is identical to the graph of y = cos x. y x
y = cos (–x)
y = cos (–x)

13. Key points:

14. 8.2 Sine and Cosine Curves
Assignment:
p. 305 #1-9 odd

15. Period and Amplitude Changes
8.2 Sine and Cosine Curves
Period and Amplitude Changes

16. 8.2 Sine and Cosine Curves Objectives: Vocabulary:
Evaluate sine and cosine functions with amplitude and period changes
Identify Period and Amplitude from a graph
Write the equation or a trig function from a graph
Vocabulary:
Amplitude, period

17. Examples

18. Writing an Equation

19. Writing an Equation

20. Writing an Equation

21. Writing an Equation

22. 8.2 Sine and Cosine Curves
Assignment:
p. 305 #11-17 odd, 27, 29