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.
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