Thread: determining vertical translation (graphing sine, cosine, and tangent)

1. determining vertical translation (graphing sine, cosine, and tangent)

hello!

I need help in answering this question

a cosine fxn has a maximum value of 7
and a minimum value of -3

a: determine amplituted

7--3/2=5 amplitude

b: determine the vertical translation:
how?

c: final equation and graph the fxn

so far i got y=5cos

2. Originally Posted by jepal
hello!

I need help in answering this question

a cosine fxn has a maximum value of 7
and a minimum value of -3

a: determine amplituted

7--3/2=5 amplitude

b: determine the vertical translation:
how?

c: final equation and graph the fxn

so far i got y=5cos
The mean value between -3 and 7 is 2. That means the x-axis is translated up by 2 units. Therefore the final result should be:

$\displaystyle y = 2+5\cos(x)$

3. Originally Posted by earboth
The mean value between -3 and 7 is 2. That means the x-axis is translated up by 2 units. Therefore the final result should be:

$\displaystyle y = 2+5\cos(x)$
Ok thanks but shouldnt the answer be
$\displaystyle y =5\cos(x)+2$[/quote]
or does it even matter. Also will this be the case all the time, to determine the vertical translation, u just find the average of the max and min value? also, what is the reasoning behind the mean=vertical translation? Thank you again.

4. Originally Posted by jepal
Ok thanks but shouldnt the answer be
$\displaystyle y =5\cos(x)+2$ or does it even matter (1). Also will this be the case all the time, to determine the vertical translation, u just find the average of the max and min value? (2) also, what is the reasoning behind the mean=vertical translation? Thank you again.
to (1): The addition is commutative so the order of the summands doesn't matter.

to (2): The cos-function is symmetric to the x-axis, that means it bisects the distance between the maximum and the minimum of the function.
If you calculate the mean value between min and max you actually locate where the axis of symmetry is and you can determine the direction and the distance of the translation.