2. 6.6 Notes.notebook April 09, 2013
6.6 Combined Trig Transformations
When looking at multiple transformations on a trig graph,
the form is :
y=a sin(b(xh))+k
a: amplitude (vertical stretch) from
k: vertical shift
b: no. of cycles in (for sine and cosine)
h: horizontal shift
Remember that When given the equation we can
therefore find the period size.
By manipulating this statement we also get When
given the graph and determining the period we can therefore
find the b value to write the equation.
Apr 139:41 AM
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3. 6.6 Notes.notebook April 09, 2013
Ex)
What is the period and draw a sketch of :
y=cos(4x)
Find the b value to help write the equation of this graph.
Apr 139:56 AM
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4. 6.6 Notes.notebook April 09, 2013
The easiest way to sketch a trig graph after multiple transformations
is to:
1) analyze the vertical shift
2) apply the vertical stretch (amplitude) to this shift
3) determine the horizontal shift as a starting point of the trig function.
Remember that sine starts in "the middle" while cosine starts at "the top".
4) Use "b" to determine "p" to draw a complete cycle of the function
Apr 139:58 AM
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5. 6.6 Notes.notebook April 09, 2013
Let's begin by sketching some trig functions with only
2 transformations. Use the supplied graph paper.
a) y=3sin(x) + 2
b) y=4cos(x) 1
c) y=5sin(2x)
d) y=cos2(x )
e) y=sin (3x6) This one has an issue!
Apr 1310:16 AM
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13. 6.6 Notes.notebook April 09, 2013
Now let's work from a given graph back to an equation.
Determine the values of a, b, h, and k, and substitue into
the general form of the trig equation.
NOTE: You can use either sine or cosine, and can also
reflect them to fit the graph.
a= ____________
p=_____ b=________
h= ___________
k= ___________
Apr 1310:16 AM
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