SOLUTION: write a cosine function with amplitude 3 and period pi/2 which has been shifted up 1 unit.

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Question 1141704: write a cosine function with amplitude 3 and period pi/2 which has been shifted up 1 unit.

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52848) About Me  (Show Source):
You can put this solution on YOUR website!
.
f(x) = 3*cos(4x) + 1.


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


With no horizontal shift, a general cosine function is

f%28x%29+=+a%2Acos%28bx%29%2Bd

where a is the amplitude, b determines the period, and d is the vertical shift.

In this problem the amplitude is 3 and the vertical shift is +1, so the equation is

f%28x%29+=+3%2Acos%28bx%29%2B1

To find the value of the parameter b, note that the basic cosine function has a period of 2pi while the given function has a period of pi/2. That means the function completes 4 cycles from 0 to 2pi; that means b is 4.

(Algebraically, b is equal to 2pi divided by the period; in this example, (2pi)/(pi/2) = 4.)

So

f%28x%29+=+3%2Acos%284x%29%2B1%29