4 5 graphs of sine and cosine function-0
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4.5 Graphs of Sine and4.5 Graphs of Sine and
Cosine FunctionsCosine Functions
AmplitudeAmplitude
PeriodPeriod
TranslationsTranslations
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The graph of f(x)sin x
!omain all "eal num#ers
"ange $% to %
1,
2
1,
2
3
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The graph of f(x)sin x
Sin x is an odd function
1,2
1,2
1,2
3
1,
2
3
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Graph of f(x) $sin x
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Graph of the f(x) Cos x
!omain& All real num#ers
"ange& $% to %
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Graph of the f(x) Cos x
Cos x is an e'en function
( )1,( )1,
( )1,2( )1,2
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The red graph is Sin and the #lue is Cos
== xxfxxf2
sin)()cos()(
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Amplitude changes the "ange
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Amplitude changes the "ange
Since Amplitude is a distance it is ala*s
positi'e.
To find it& the a#solute 'alue of the
+aximum minus the +inimum di'ide #*
to.
Amp is ritten #efore the function
* a,sin x
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Amplitude changes the "ange
+ax - +in $ % Amp.
1,2
7,
2
42
)1(7=
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Period (a'e length)
The distance #efore the function repeats its
'alue. * sin #x here # is %.
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Period (a'e length)
* sin /x # /
periodb
=2
1,4
1,4
5
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Translation to mo'e the graph of the
function * sin (x 0 c)&
mo'es "ight or 1eft
2ere is
+=2
sin
xy
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Translation to mo'e the graph of the
function* sin x 0 d
mo'es up or don
2ere is 2sin += xy
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3ith all the translations
The sine function is
f(x) d 0 a sin #(x 0c)
The cosine function is
f(x) d 0 a cos #(x 0c)
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Applet for the Sine function
http&.anal*6emath.comtrigonometr*
sine.htm
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Page 307 310Page 307 310
##3, 9, 14, 20,3, 9, 14, 20,
26, 32, 41, 49,26, 32, 41, 49,71, 7871, 78
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