S
ECT
4.3 C
HANGING
THE
PERIOD
IN
A
SINE
AND
COSINE
FUNCTION
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C
HANGING
THE
PERIOD
:
The period in or is
If a constant is placed in front of the x-variable, the period
will expand or compress (CEEC)
Expansion
Compression
Expansion
& Reflection
Compression
& Reflection
Ex: Indicate the period for the following trig. function:
HC by a factor of 1/3
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Practice: Find the period for each of the following trigonometric
functions:
HC by a factor of 1/2
HE by a factor of 3/2
HE by a factor of 4
Note: One way to find the period is to take
2
π
and divide it
by the constant “k” in front of
“x”
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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
For Sine functions, start at the middle
For Cosine Functions, start at the top
(unless there’s a vertical reflection
Upside down
)
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Ex: Graph the 2 cycles of the following Trigonometric
function
Repeat the cycle to
the left and right
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Practice: Graph the following Trigonometric function
Repeat the cycle to
the left
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Ex: Given the following graph, which of the following is the
correct equation
x
y
-1
1
2
3
4
5
6
First draw the vertical displacement
All equations have the same
Amplitude, so don’t worry about it
Check the Horizontal
displacement for each equation
Graph starts at the top, so it can’t
be a sine graph
Graph starts at the middle, so it can’t
be a cosine graph
Graph should start at the bottom because
It’s a cosine graph with a vertical reflection
This is the correct function!!
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Ex: Given that the following graph has an equation in the form of
, what is the value of B ?
Draw the Vertical Displacement
Find the length of the period
Each increment is
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Challenge: Given that the coordinates (
m,n
) is on the
given sine function, then which of the following points
will also be on the function?
x
y
-1
1
The period of the function is:
Whenever you add/subtract the period from the a certain
point, you reach the next cycle and the Y-coordinate stays
consistent
To find a point that’s also on the graph, just add the
Period to the X-coordinate:
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Challenge: Given that the coordinates (
m,n
) is on the
function y = sin(x), which of the following points will be
on the function after the transformation?
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V.E. by a factor of 4
Multiply the Y-coordinate by 4
H. Compression by 2
Multiply the X-coordinate by ½
H.S. of 5 units right
Add 5 to the x-coordinate
H
OMEWORK
:
P254 #2,3,7,8,11,12,14-17, 19, 22
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