SOLUTION: In this sinusoidal function 2 cos (2x -60) + 2
What is:
a)
Max. Value:
Min. Value:
Amplitude:
Period:
Phase Shift:
Equation of Axis:
b) Sketc
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Points-lines-and-rays
-> SOLUTION: In this sinusoidal function 2 cos (2x -60) + 2
What is:
a)
Max. Value:
Min. Value:
Amplitude:
Period:
Phase Shift:
Equation of Axis:
b) Sketc
Log On
the general equation is y = a * cos (b * (x - c)) + d
a is the amplitude.
b is the frequency
c is the horizontal shift
d is the vertical shift.
to make your equation look like the general equation, factor out a 2 from 2 * x - 60 to get 2 * (x - 30).
this makes you equation equal to 2 * cos (2 * (x - 30)) + 2
since the general equation is y = a * cos (b * (x - c)) + d, it's now easy to see that>
a = 2
b = 2
c = 30
d = 2
that means you amplitude is plus or minus 2 units from the center line of the equation; your frequency is 2 full cycles of the cosine wave in 360 degrees; your horizontal shift is 30 degrees to the right; your vertical shift is 2 units above the center line.
i'll show this on the graph in separate steps so you can see what happens.
i'll start with y = cos (x)
next is y = 2 * cos(x).
the amplitude has been doubled so the positive peaks are 2 units from the center line and the negative peaks are also 2 units from the center line of of y = 0
next is y = 2 * cos(2 * x)
everything is the same as last graph except the frequency is 2 and you therefore have two full cycles of the cosine wave in 360 degrees.
next is y = 2 * cos(2 * x) + 2
everything is the same as the last graph except the center line has shifted from y = 0 to y = 2.
next is y = 2 * cos(2 * (x - 30)) + 2
everything is the same as the last graph except the start of the first full cosine wave is now 30 degrees instead of 0 degrees, and the start of the second full cosine wave is now 210 degrees instead of 180 degrees.
