Learning to Read the Wave Riding the Perfect Wave by flickr user San Diego Shooter
Jun 20, 2015
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