homework questions. section 4.4 graphing sin(x) and cos(x) investigation first! investigation first!...
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Homework QuestionsHomework Questions
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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 Do sin(x) only to get started…started…
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Periodic:Periodic:
A function is periodic if for some A function is periodic if for some real number real number αα, f (x+ , f (x+ αα) = f (x) for ) = f (x) for each x in the domain.each x in the domain.
The least positive value for The least positive value for αα for for which f (x+ which f (x+ αα) = f (x) is the ) = f (x) is the periodperiod of the function. of the function.
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Examples…Examples…
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Graph on your calc:Graph on your calc:
y = sin(x) and determine if y = sin(x) and determine if periodicperiodic
(ZOOM – TRIG)(ZOOM – TRIG)
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Properties of sin(x)Properties of sin(x)
Period = 2Period = 2ππ Domain: (-∞, ∞)Domain: (-∞, ∞) Range: [-1, 1]Range: [-1, 1]
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Graph cos xGraph cos x
On investigation sheet first…On investigation sheet first…
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Graph cos xGraph cos x
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Properties of cos(x)Properties of cos(x)
Period = 2Period = 2ππ Domain: (-∞, ∞)Domain: (-∞, ∞) Range: [-1, 1]Range: [-1, 1]
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Section 4.4Section 4.4
Translating sin and cosTranslating sin and cos
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AmplitudeAmplitude
The amplitude of the functions The amplitude of the functions
y = A sin y = A sin ӨӨ and and y = A cos y = A cos ӨӨ is the is the absolute value of A.absolute value of A.
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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 go The distance it takes to go ““one one
wavewave””
b
2
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State the amplitude State the amplitude and the period and and the period and graph:graph:
2
cos4
y
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State the amplitude State the amplitude and the period and and the period and graph:graph:
4sin2
1y
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State the amplitude State the amplitude and the period and and the period and graph:graph:
3
cos2
y
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State the amplitude State the amplitude and the period and and the period and graph:graph:
xy 2sin2
3
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One last thing…One last thing…
Write an equation of the Write an equation of the cosine function with amplitude cosine function with amplitude 9.8 and period 69.8 and period 6ππ..
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HomeworkHomework
P. 394 (1-15 odd) - donP. 394 (1-15 odd) - don’’t graph, t graph, just state information (17-28) – just state information (17-28) – State all information and graph State all information and graph one period.one period.
Sticker assignment – posted Sticker assignment – posted onlineonline