Aim: How do we sketch the graphs of y = asin(bx + c) + d and y = a cos(bx + c) + d ?
y = sin(.5x) -5 between [- π, 2π]
Feb 28­5:01 PM
(Phase Shifts)
amplitude a
II
horizontal shift + shifts left
­ shifts right
y = a sin (bx ­ c) + d
frequency
vertical shift + shifts up
­ shifts down
Explain the Shift of the graph of y=sin(2x ­ π )
2
Mar 5­11:16 AM
HORIZONTAL
Example 1: Sketch the graph of y=sin(x ­ π ) for 2 full cycles
2
State the following:
amp =
freq =
period =
1/4 pd =
Phase shift =
LE=
Keep in mind: LE is the starting interval
Feb 27­9:17 PM
Trig Functions on GSP.gsp
Feb 28­4:52 PM
Ex 2: Sketch the graph of y = 2cos (2x - π)
2
State the following:
amp =
freq =
period =
1/4 pd =
Phase shift =
LE=
Feb 27­9:34 PM
PHASE SHIFT = horizontal translation of a periodic function.
Feb 28­4:30 PM
Ex 3: Find the amplitude, period, and phase shift
for the sine function shown in the diagram.
Write an equation for this graph.
3
­1.57
4.72
­3
Mar 2­8:40 AM
Homework:
Sketch the graph of y = 2cos (x + π) between [- π, π]
State the following:
amp =
freq =
period =
1/4 pd =
Phase shift =
LE=
Feb 27­9:34 PM
Homework:
Example : Sketch the graph of y=3sin(2x + π )
for 2 full cycles 2
State the following:
amp =
freq =
period =
1/4 pd =
Phase shift =
LE=
Mar 4­6:53 PM
Aim: How do we sketch the graphs of y = asin(bx + c) + d and y = a cos(bx + c) + d ?
Do NOW: Find the amplitude, period, and
phase shift for the cosine function shown in
the diagram. Write an equation for this
graph.
5
2π
­2π
­5
Mar 2­8:40 AM
Graph (2 Cycles)
6) y = 3sin (x ­ π) +4
2
amp =
freq =
period =
1/4 pd =
Phase shifts =
Feb 28­5:48 PM
Graph (2 Cycles)
7) y = cos (2x + π ) - 4
amp =
2
freq =
period =
1/4 pd =
Phase shifts =
Feb 28­5:48 PM
Homework:
graph of y = -3sin (x - π) - 4
4
(for 2 cycles)
graph of y = 4cos (x + π) + 2
3
(for 1 cycle)
Mar 15­2:02 PM
Attachments
Trig Functions on GSP.gsp