january 24 th copyright2009merrydavidson. y = cos x
TRANSCRIPT
January 24th copyright2009merrydavidson
y = cos x
y = D - A trig function B ( + C)
Horizontal
shift “C”
units “right or left”
Affects
x-values
Determines the period.
Affects
x-values
Amplitude
Affects
y-valuesVertical shift
Affects
y-values
Negative sign means reflect over the x-axis
AMPLITUDE
Is the Positive height of the trig graph.
A
y = D - A trig function B ( + C)
What is the amplitude of the sine parent graph? 1
At the origin, middle, high, middle, low.
y = cos x
What is the amplitude of the cosine parent graph?
1
At the origin, high, middle, low, middle.
On your class worksheet
Fill in the amplitude for all 10 equations.
PHASE SHIFT: Horizontal (L or R)
The start point has shifted pi/2 to the right.
( ) sin( )2
f x x
y = D - A trig function B ( + C)
On your class worksheet
Fill in the phase shift for all 10 equations. Phase shift is always “inside” of the parenthesis.
VERTICAL SHIFT: up or down
Now the start point is at y=2.
The sine curve shifted up 2.( ) sin 2f x x
y = D - A trig function B ( + C)
On your class worksheet
Fill in the vertical shift for all 10 equations. Vertical shift is in the front or the back.
Be careful with signs!
y = D - A trig function B ( + C)
Will this be graphed in degrees or radians?
degrees
Use x for radians and
theta for degrees.
PERIOD: Length of 1 cycle (when you get back to the start position.)
PERIOD for sine and cosine parent function is
360o or 2 pi radians.
When you put transformations on the parent function the period changes.
PERIOD:How long it takes to repeat the pattern. (get back to the start position)
It took Pi units to get back to the middle. So the period of this graph is pi.
You use “B” to find
360 2o
P RB B
the period of the transformed function.
y = D - A trig function B ( + C)
On your class worksheet
Fill in the Period for all 10 equations.
Write an equation for a positive sine curve with an amplitude of 3, period of 90 and
phase shift of 45 right. Start with the equation…
y = D + A trig function B ( + C)
Amplitude of 3 does what?
3
Our trig function is sine.
y = sin
Phase shift now
( - 45)
Period of 90.
4
Write a possible equation for a positive cosine curve with an amplitude of 4, period of
4, and phase shift of /2 right. Start with the equation…
y = D + A trig function B ( + C)
Amplitude of 4 does what?
4
Our trig function is cosine.
y = cos x
Phase shift now
( - /2)
Period of 4 .
HW: WS 7-1