![Properties of sin(x)Properties of sin(x)
Period = 2Period = 2ππ
Domain: (-∞, ∞)Domain: (-∞, ∞)
Range: [-1, 1]Range: [-1, 1]](https://image.slidesharecdn.com/graphingday1worked-161020140456/85/Graphing-day-1-worked-6-320.jpg)
![Properties of cos(x)Properties of cos(x)
Period = 2Period = 2ππ
Domain: (-∞, ∞)Domain: (-∞, ∞)
Range: [-1, 1]Range: [-1, 1]](https://image.slidesharecdn.com/graphingday1worked-161020140456/85/Graphing-day-1-worked-9-320.jpg)
Graphing day 1 worked
- 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.
- 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