S
ECT
4.4 G
RAPHING
S
INE
/C
OSINE
F
UNCTIONS
WITH
H
ORIZONTAL
C
OMPRESSIONS
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I
) R
EVIEW
:
Ex: Indicate the transformation for each of the following
equation:
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II) G
RAPHING
When a constant is placed before the x-variable in a trig.
function, a H.E. or H.C. will occur (depending on the value
on the constant: CEEC)
If
Horizontal Expansion
If
Horizontal Compression
When 2
π
is placed before the x-variable, the graph will
undergo a H.C. by a factor of . So the period will
compress from 2
π
to 1
x
-1
-0.5
0.5
1
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When graphing the constant “p” is the period
The constant
2
π
will Horizontally compress the period from
2
π
to
1
The constant “
p
” in the denominator will horizontally expand
the period from 1 to length “
p
”
Ex: Indicate the period for each of the following trig. functions:
Solve for
“p”
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Ex: Graph 2 cycles of each of the following functions:
x
-1
-0.5
0.5
1
x
-1
-0.5
0.5
1
Find the period
Period is 5 units
long
Find the period
Period is 3.33 units
long
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Ex: Given that each of the following graphs is in the form of
, find the value of “B”
x
y
-1
1
x
y
-1
0
1
2
3
4
5
6
7
8
9
-1
1
x
y
-1
0
1
2
3
4
-1
1
The period is 6
π
The period is 5
2.5 cycles of the period is equal to 3
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R
EVIEW
: S
TEPS
FOR
G
RAPHING
T
RIGONOMETRIC
F
UNCTIONS
:
Find the vertical displacement “D” and draw a line for
Use the amplitude to draw the Maximum horizontal line
and Minimum horizontal line
Use the horizontal displacement “C” to find where the
graph will start
Use the period “p” to map out how long one cycle of the
function. Cut the cycle into 4 sub-domains
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Ex: Graph the 3 cycles of the following function:
Repeat the cycle to
the left and right
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x
y
-5
-4
-3
-2
-1
1
Practice: Graph the 3 cycles of the following function:
Repeat the cycle to
the left and right
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Challenge: Given the following graph, which of the following is
the correct equation?
x
y
-2
-1
0
1
2
3
4
5
6
7
-1
1
2
3
4
5
Find the V.D., Amplitude, Period of the graph
Simplify each equation:
Graph each equation
The first equation works!!!
The second equation works!!!
The third equation also works!!!
All 3 equations will work!!!
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H
OMEWORK
:
P265 – 269 #1-5, 7, 14-16, 20, 22, 26
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