Homework Questions
Section 4.4
Graphing sin(x) and cos(x)
•Investigation FIRST!
•Input/Output discussion
•Do sin(x) only to get started…
Periodic:
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A function is periodic if for some real
number α, f (x+ α) = f (x) for each x
in the domain.
The least positive value for α for which
f (x+ α) = f (x) is the period of the
function.
Examples…
Graph on your calc:
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
y = sin(x) and determine if periodic
(ZOOM – TRIG)
Properties of sin(x)
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Period = 2π
Domain: (-∞, ∞)
Range: [-1, 1]
Graph cos x

On investigation sheet first…
Graph cos x
Properties of cos(x)
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

Period = 2π
Domain: (-∞, ∞)
Range: [-1, 1]
Section 4.4
Translating sin and cos
Amplitude

The amplitude of the functions
y = A sin Ө and y = A cos Ө is the
absolute value of A.
2
Period = b

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y = a sin (bx +c) + d
y = a cos (bx +c) + d
The distance it takes to go “one
wave”
State the amplitude and
the period and graph:
 
y  4 cos 
2
State the amplitude and
the period and graph:
1
y  sin 4 
2
State the amplitude and
the period and graph:
 
y  2 cos 
3
State the amplitude and
the period and graph:
3
y
sin 2 x 
2
One last thing…

Write an equation of the cosine
function with amplitude 9.8 and
period 6π.
Homework

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P. 394 (1-15 odd) - don’t graph, just
state information (17-28) – State all
information and graph one period.
Sticker assignment – posted online