Transcript Section 4.5 Graphs of Sine and Cosine Functions Continuation of the previous problem showing 3 cycles.

Section 4.5
Graphs of Sine and Cosine
Functions
Continuation of the previous problem showing 3 cycles
Graphing y=2 Sin x
Graphing y=½ Sin x
Graphing y=-2 Sin x
Graphing y=3 Sin 2x
The Effect of Horizontally Shifting the Graph
Example
Determine the amplitude and period of the following
and graph:
1
y  sin 3x
4
Example
Determine the amplitude and period of the following
and graph:
y=-2sin 2x
Example
Determine the amplitude and period of the following
and graph the function :
y  3sin  x
y




x













Example
Determine the amplitude and period of the following
and graph the function :
y  4 sin 2 x
y




x













Example
Determine the amplitude, period and phase shift
of the following and graph the function :
y  2sin  4x+ 
Example
Determine the amplitude, period and phase shift
of the following and graph the function :
1 

y  sin  2x - 
2 
2
Cosine with a Different Amplitude and Period
Example
Determine the amplitude and period of y=-2cos4x
Example
Determine the amplitude, period, and phase shift
of y=2cos  3x   
Vertical Shifts
of
Sinusoidal Graphs
Cosine Function with a Vertical Shift
Example
Determine the amplitude and period of y=-2cos(4x)+1
Example
Determine the amplitude, period, and phase shift
of y=2cos  3x   1
Example
Tides are very high in some areas of Canada. The depth of
the water at a boat dock in Nova Scotia varies from a high
tide of 20 feet to a low tide of 6 feet. On a certain day high
tide is at 2 AM. and low tide is at 8 AM. If y represents the
depth of the water in feet, x hours after midnight, use a sine
function of the form y=Asin(Bx-C)+D to model the water's
depth.
20
10
2
6
10
14
18
The number of hours after midnight.
22
26
Find the amplitude of y=-3sin 2 x
(a) 1
(b) 2
(c)  3
(d) 3
Find the period of y=-3sin 2 x
(a) 1
(b) 2
(c)  3
(d) 3
What is the phase shift of y=-2cos  2x   .
(a) -2
(b) 2
(c) 1
(d) 

2