Graphing Day 1

1. Homework QuestionsHomework Questions

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

3. Periodic:Periodic:
 A function is periodic if for some realA function is periodic if for some real
numbernumber α, f (x+ α) = f (x) for each x inα, f (x+ α) = f (x) for each x in
the domain.the domain.
 The least positive value for α for whichThe least positive value for α for which
f (x+ α) = f (x) is thef (x+ α) = f (x) is the periodperiod of theof the
function.function.

4. Examples…Examples…

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

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

7. Graph cos xGraph cos x
 On investigation sheet first…On investigation sheet first…

8. Graph cos xGraph cos x

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

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

11. AmplitudeAmplitude
 The amplitude of the functionsThe amplitude of the functions
y = A siny = A sin Ө andӨ and y = A cosy = A cos Ө is theӨ is the
absolute value of A.absolute value of A.

12. Period =Period =
 y = a sin (bx +c) + dy = a sin (bx +c) + d
 y = a cos (bx +c) + dy = a cos (bx +c) + d
 The distance it takes to goThe distance it takes to go ““one waveone wave””
b
π2

13. State the amplitude andState the amplitude and
the period and graph:the period and graph:






=
2
cos4
π
y

14. State the amplitude andState the amplitude and
the period and graph:the period and graph:
( )Θ= 4sin
2
1
y

15. State the amplitude andState the amplitude and
the period and graph:the period and graph:






=
3
cos2
π
y

16. State the amplitude andState the amplitude and
the period and graph:the period and graph:
( )xy 2sin
2
3−
=

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

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