SOLUTION: State the amplitude, period, phase shift, and equation of midline/axis of curve, x and y axis for f(x) = 3cos(1/2x+90) −1

Algebra ->  Functions -> SOLUTION: State the amplitude, period, phase shift, and equation of midline/axis of curve, x and y axis for f(x) = 3cos(1/2x+90) −1      Log On


   

Question 1182157: State the amplitude, period, phase shift, and equation of midline/axis of curve, x and y axis for f(x) = 3cos(1/2x+90) −1
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


f%28x%29+=+3cos%28%281%2F2%29x%2B90%29%29-1

Rewrite the function so the coefficient on x is 1:

f%28x%29+=+3cos%28%281%2F2%29%28x%2B180%29%29-1

That is in the form

f%28x%29+=+a%2Acos%28b%28x-c%29%29%2Bd

In that form...

a is the amplitude
b determines the period (the period (in degrees) is 360/b)
c is the horizontal shift (phase shift)
d is the vertical shift (determines the midline)

So in this function...

a is 3
b is 1/2; the period is 360/b = 360/(1/2) = 720 degrees
c is -180 degrees
d is -1

ANSWERS:
amplitude 3
period 720 degrees
phase shift -180 degrees
midline y=-1