State the Period, Amplitude, Phase Shift, Vertical Shift, and equation (using cosine
Your question is incomplete.
For a wave equation in the form
Y(t) = A cos[2*pi*t/P -(phi)] + B
P is the period
A is the amplitude
phi is the phase shift, and
B is the vertical shift
f(x) = A sin(B(x - C)) + D or f(x) = A cos(B(x - C)) + D that's the equation
A Amplitude: Maximum y-coordinate – minimum y-coordinate divided by 2
( Max y – Min y)/2
B Adjustment for period change: B =
2
Period
π
C Phase shift: Right or left x - transformation
D Vertical shift: Maximum y-coordinate + minimum coordinate divided by 2
( Max y + Min y)/2
Use Cosine
Use Sine
You can readily determine the maximum and/or minimum points.
You can readily determine the horizontal axes points
I don't understand this at all
It might be a good idea to look at different graphs of
f(x) = sin x
This webpage lets you see more than one graph on the same grid
http://rechneronline.de/function-graphs/
set "Range x-axis from" to -3.14 to 6.28 ( -π to 2π)
set "Range y-axis from" to -5 to +5
in the first graph window enter
sin(x)
press the ENTER key and take a look at it, and see how many cycles you have from 0 to 6.28
in the "second graph" window, enter
2*sin(x)
---- What do you notice?
Now try the following entries in "second graph"
-2*sin(x)
sin(3x)
2*sin(3x)
2*sin(3x) + 1
2*sin(3x) -2
3*sin(2x)
sin(x-2)
sin(x+2)
4sin(2*(x-1.5) - 2
The last will have
amplitude = 4
period = 2π/2=π (there should be 2 complete cycles from -π to +π )
vertical shift = -2 , it went down 2 units
horizontal shift = 1.5 units to the right
make up your own variations with the second graph
repeat the same exercise using the cosine function
cos(x)