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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 $ ,