1. Homework Questions

2. Section 4.4 Graphing sin(x) and cos(x) Investigation FIRST!
Input/Output discussion
Do sin(x) only to get started…

3. Periodic:
A function is periodic if for some real number α, f (x+ α) = f (x) for each x in the domain.
The least positive value for α for which f (x+ α) = f (x) is the period of the function.

4. Examples…

5. Graph on your calc:
y = sin(x) and determine if periodic
(ZOOM – TRIG)

6. Properties of sin(x)
Period = 2π
Domain: (-∞, ∞)
Range: [-1, 1]

7. Graph cos x
On investigation sheet first…

8. Graph cos x

9. Properties of cos(x)
Period = 2π
Domain: (-∞, ∞)
Range: [-1, 1]

10. Translating sin and cos
Section 4.4
Translating sin and cos

11. Amplitude The amplitude of the functions
y = A sin Ө and y = A cos Ө is the absolute value of A.

12. Period = y = a sin (bx +c) + d y = a cos (bx +c) + d
The distance it takes to go “one wave”

13. State the amplitude and the period and graph:

14. State the amplitude and the period and graph:

15. State the amplitude and the period and graph:

16. State the amplitude and the period and graph:

17. One last thing…
Write an equation of the cosine function with amplitude 9.8 and period 6π.

18. Homework
P. 394 (1-15 odd) - don’t graph, just state information (17-28) – State all information and graph one period.
Sticker assignment – posted online