1. Section 4.5 Graphs of Sine and Cosine

2. Key Terms
Amplitude (meters) The height of the wave or distance from the midline to the max/min. Period (seconds/ Radians) The time it takes to complete one cycle/wave. Frequency (Hertz or cycles per second, CPS) The number of waves in a given period of time. Midline (meters) The horizontal line in the middle of the wave. The average of the max and min. Y= (max+min)/2

3. The Graph of y=sin θ

4. 3 cycles of Sin graph
Graph begins at origin and goes up first (Dueling Dragons )
Domain=
Range =
Period=
Even, odd, or neither=

5. Graphing Sinusoidal Graphs Parent Function y= sin x
Transformations y= A sin (Bx –C) +D
Parent Function y= cosx
Transformations y= A cos (Bx –C) +D

6. Graphing sin Parent Function y= sin x Transformations y= A sin (Bx –C)

7. Graphing y=2 Sin x
Graphing y=½ Sin x
Graphing y=-2 Sin x

8. Graphing y=3 Sin 2x

9. Horizontal Shift of Sine
*Highlight key points

11. Example

12. Example

13. Example

14. Example

15. Example

16. Example

17. The Graph of y=cos x

18. Graphing Variations of y= cos θ
Cosine with a Different Amplitude and Period
* Starts at the top and goes out and down (The Hulk)

19. Horizontal Shift of Cosine

20. Example

21. Example

22. Vertical Shifts
Example

23. Example

24. REAL-LIFE APPLICATION
Example 20 10
The number of hours after midnight.

25. QUICK POLL
(a)
(b)
(c)
(d)

26. (a)
(b)
(c)
(d)

27. (a)
(b)
(c)
(d)