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Homework QuestionsHomework Questions
Section 4.4Section 4.4
Graphing sin(x) and cos(x)Graphing sin(x) and cos(x)
•Investigation FIRST!Investigation FIRST!
•Inp...
Periodic:Periodic:
 A function is periodic if for some realA function is periodic if for some real
numbernumber α, f (x+ ...
Examples…Examples…
Graph on your calc:Graph on your calc:
 y = sin(x) and determine if periodicy = sin(x) and determine if periodic
 (ZOOM ...
Properties of sin(x)Properties of sin(x)
 Period = 2Period = 2ππ
 Domain: (-∞, ∞)Domain: (-∞, ∞)
 Range: [-1, 1]Range: ...
Graph cos xGraph cos x
 On investigation sheet first…On investigation sheet first…
Graph cos xGraph cos x
Properties of cos(x)Properties of cos(x)
 Period = 2Period = 2ππ
 Domain: (-∞, ∞)Domain: (-∞, ∞)
 Range: [-1, 1]Range: ...
Section 4.4Section 4.4
Translating sin and cosTranslating sin and cos
AmplitudeAmplitude
 The amplitude of the functionsThe amplitude of the functions
y = A siny = A sin Ө andӨ and y = A cosy...
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 ...
State the amplitude andState the amplitude and
the period and graph:the period and graph:






=
2
cos4
π
y
State the amplitude andState the amplitude and
the period and graph:the period and graph:
( )Θ= 4sin
2
1
y
State the amplitude andState the amplitude and
the period and graph:the period and graph:






=
3
cos2
π
y
State the amplitude andState the amplitude and
the period and graph:the period and graph:
( )xy 2sin
2
3−
=
One last thing…One last thing…
 Write an equation of the cosineWrite an equation of the cosine
function with amplitude 9....
HomeworkHomework
 P. 394 (1-15 odd) - donP. 394 (1-15 odd) - don’’t graph, justt graph, just
state information (17-28) – ...
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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

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