6.6 9th april 2013
TRANSCRIPT
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6.6 Notes.notebook
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April 09, 2013
Apr 912:35 PM
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April 09, 2013
Apr 139:41 AM
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) fromk: vertical shiftb: 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 thereforefind the b value to write the equation.
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April 09, 2013
Apr 139:56 AM
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.
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April 09, 2013
Apr 139:58 AM
The easiest way to sketch a trig graph after multiple transformationsis to:1) analyze the vertical shift2) apply the vertical stretch (amplitude) to this shift3) 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
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Apr 1310:16 AM
Let's begin by sketching some trig functions with only2 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!
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April 09, 2013
Apr 912:57 PM
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April 09, 2013
Apr 91:04 PM
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Apr 91:15 PM
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Apr 91:29 PM
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a=_________
b=______ p=_______
c= ________
d= ________
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Apr 1310:07 AM
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Apr 1310:16 AM
Now let's work from a given graph back to an equation.Determine the values of a, b, h, and k, and substitue intothe general form of the trig equation.
NOTE: You can use either sine or cosine, and can alsoreflect them to fit the graph.
a= ____________
p=_____ b=________
h= ___________
k= ___________
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Apr 1310:27 AM
a=
b= p=
h=
k=
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April 09, 2013
Apr 1310:34 AM
Write this graph as BOTH a sine and a cosine function!
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Apr 1310:35 AM
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HOMEWORK: Pg. 535 #4, 5, 6,7, 8a), 9a) 10 (for sketching in 10, draw one complete cycle)