Graphing Sine and Cosine Functions Blank Notes - Inver Hills Community ...
Graphing Sine and Cosine Functions Video Lecture
Sections 6.4 and 6.6
Course Learning Objectives: Demonstrate an understanding of trigonometric functions and their applications.
Weekly Learning Objectives: 1) Graph functions of the form y=a(sinbx+c)+d using transformations. 2) Graph functions of the form y=a(cosbx+c)+d using transformations. 3) Determine the domain, range, amplitude, period, intercepts, extrema and symmetry of sinusoidal functions. 4) Graph sinusoidal functions using key points. 5) Find an equation for a sinusoidal graph.
Graphing the Sine and Cosine Functions
0 B oe sin B
Note: sin ?> #81? oe sin > We say sin > has a period of 21
B sin B B sin B B sin B B sin B
!
#1 $
(1 '
&1 $
1
$1
&1
(1
'
%
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1
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""1
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1
1
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$1 #
#1
Domain: Period:
Range: Intercepts:
page 1
Symmetry: Extrema
All previously discussed transformations apply to all trigonometric functions. The most general form of the equation is
0 B oe + sin ?,B
-?
. oe + sin ,?B
,
?
.
+pvertical stretch/compression (amplitude)
,phorizontal stretch/compression (period)
,
phorizontal
translation
(phase shift)
.pvertical translation
Indicate the transformations implied and sketch the graph of each of the following:
0 B oe # sin B
page 2
1 B oe sin #B
6 B oe sin B
4 B oe $ sin ?B
1 %
?
page 3
2 B oe sin B #
< B oe sin ? B? "
> B oe # sin ?$B
1 #
?
page 4
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