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# Graphing day 1 worked

Graphing Day 1

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### Graphing day 1 worked

1. 1. Homework QuestionsHomework Questions
2. 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. 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. 4. Examples…Examples…
5. 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. 6. Properties of sin(x)Properties of sin(x)  Period = 2Period = 2ππ  Domain: (-∞, ∞)Domain: (-∞, ∞)  Range: [-1, 1]Range: [-1, 1]
7. 7. Graph cos xGraph cos x  On investigation sheet first…On investigation sheet first…
8. 8. Graph cos xGraph cos x
9. 9. Properties of cos(x)Properties of cos(x)  Period = 2Period = 2ππ  Domain: (-∞, ∞)Domain: (-∞, ∞)  Range: [-1, 1]Range: [-1, 1]
10. 10. Section 4.4Section 4.4 Translating sin and cosTranslating sin and cos
11. 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. 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. 13. State the amplitude andState the amplitude and the period and graph:the period and graph:       = 2 cos4 π y
14. 14. State the amplitude andState the amplitude and the period and graph:the period and graph: ( )Θ= 4sin 2 1 y
15. 15. State the amplitude andState the amplitude and the period and graph:the period and graph:       = 3 cos2 π y
16. 16. State the amplitude andState the amplitude and the period and graph:the period and graph: ( )xy 2sin 2 3− =
17. 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. 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