How do you determine the amplitude, period and vertical translation of y+2=4cos(x/2)

Ethen Frey 2022-07-23 Answered
How do you determine the amplitude, period and vertical translation of y + 2 = 4 cos ( x 2 )?
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Answers (1)

Cheyanne Charles
Answered 2022-07-24 Author has 13 answers
I would write your function isolating y as:
y = 4 cos ( x 2 ) 2
From this you can "see":
1] The amplitude of your cosine is 4 (the number in front of cos);
2] The period is 4 π ; by using the 1 2 inside the argument of cos you get:
p e r i o d = 2 π 1 2 = 4 π
3] The vertical translation is given by -2 telling you that your cos oscillates about the horizontal line passing through y=-2 (instead of oscillating about the x axis).
Graphically:
graph{ 4 cos ( x / 2 ) 2 [ 16.02 , 16.02 , 8.01 , 8.01 ]}
As you can see you have a cosine oscillating between 2 and -6 about the horizontal line at y=-2 and one complete oscillation now takes 4 π to be completed.
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