Graphing Form of Sine and Cosine Functions
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Transcript of Graphing Form of Sine and Cosine Functions
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8/9/2019 Graphing Form of Sine and Cosine Functions
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Graphing Form of Sine and
Cosine Functions
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Period
The length of one cycle of a graph.
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Initial Trigonometric Graphing Form
( )sin y a x h k = +Sine
Cosine
( )cos y a x h k = +
Do notwrite these
on yourworksheetyet. Westill need
to add onemore
parameter.
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e!uirements for a Sine"Cosine Graph
#$intercept
%t least one Period
&in other words' at least ( consecuti)ecritical points accurately plotted*
+
,
-(
%rrows&to showthat there
infinitecycles*
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a / +01a1+a 1 0Amplitude:
Half of thedistance betweenthe maximum andminimum valuesof the range of aperiodic function
with a boundedrange.
The amplitude is the absolute value of a! It is apositive distance.
The %mplitude and the 2ffect of 3a4
a 5 +
+ %mplitude 5
- 0.( +( )0.5sin y x=
( )3sin y x=
( )sin y x= ( )sin y x=
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2#ample6 Sine
( )32sin y x = +y = 0
x = - "#
Transformation6 Flip the parent graph andtranslate it -Pi", units to the left.
Transformation6
2
2
7ew 2!uation6
Period6
2
8ou need at least ( consecuti)e critical points.
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2#ample6 Cosine
( )2cos 1 y x = + y = -$
x = - "#
Transformation6 Translate the parent graph Pi",units to the left and + unit down.
Transformation6
2
2
7ew 2!uation6
Period6
2
8ou need at least ( consecuti)e critical points.
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Cosine
Sine ) Cosine
Sine
%&ress the 'raph(
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Translation $ - units up and 9
2#ample6 Sine or Cosine:
y =
7ew 2!uation6
Transformation6
2 2
%mplitude $ ,
;rientation $
Graph $
Period $ ,