applied 40s may 25, 2009
DESCRIPTION
Transformations of the sine function.TRANSCRIPT
Learning to Read the Wave
Riding the Perfect Wave by flickr user San Diego Shooter
Generate a sinusoidal equation and sketch the graph for the following set of data. Write the values of the parameters in your equation to two decimal places. Homework
Source: Winnipeg weather statistics
Month J F M A M J J A S O N Dmm 19 15 23 36 60 84 72 75 51 30 21 19
Amount of Precipitation in Winnipeg (in mm)
Generate a sinusoidal equation and sketch the graph for the following set of data. Write the values of the parameters in your equation to two decimal places. Homework
Year 0 1 2 3 4 5 6 7 8Population 200 188 160 132 120 133 161 187 201
The data below show the population of a species of marmot in a given area over a 9-year period on June 1st of each year.
Properties and Transformations of the sine function ...
Let's look at some graphs ...http://fooplot.com
ƒ(x) = AsinB(x - C) + D
D is the sinusoidal axis, average value of the function, or the vertical shift.
The Role of Parameter D
D < 0 the graph shifts down D units.D > 0 the graph shifts up D units.
The amplitude is the absolute value of A; |A|. It is the distance from the sinusoidal axis to a maximum (or minimum). If it is negative, the graph is reflected (flips) over the sinusoidal axis.
The Role of Parameter A
y = 2sin(x)
y = -3sin(x)
y = 1 sin(x) 2
Properties and Transformations of the sine function ...
Let's look at some graphs ...http://fooplot.com
ƒ(x) = AsinB(x - C) + D
y = 2sin(x) + 3
B is not the period; it determines the period according to this relation: The Role of Parameter B
or
y = sin(3x)
y = sin(2x)
C is called the phase shift, or horizontal shift, of the graph.
The Role of Parameter C
y = sin(x - π ) 4
y = sin(x + π ) 4
In general form, the equation and graph of the basic sine function is:
Note that your calculator displays: ƒ(x) = asin(bx - c) + d
Which is equivalent to: ƒ(x) = AsinB(x - c/b) + D
A=1, B=1, C=0, D=02π-2π -π π
The "starting point."
ƒ(x) = AsinB(x - C) + D
How many revolutions (in radians and degrees) are illustrated in each graph?
How many periods are illustrated in each graph?
Periods = Radians Rotated = Degrees Rotated =
Periods = Radians Rotated = Degrees Rotated =
Periods = Radians Rotated = Degrees Rotated =
HOMEWORK
Determine approximate values for the parameters 'a', 'b', 'c', and 'd' from the graphs, and then write the equations of each graph as a sinusoidal function in the form: y = a sin b(x - c) + d Remember
"DABC!"
HOMEWORK
State the amplitude, period, horizontal shift, and vertical shift for each of the following:
amplitude: period: horizontal shift:vertical shift:
amplitude: period: horizontal shift:vertical shift:
HOMEWORK