Find the amplitude, period, phase shift, and vertical displacement for y= square root of 7 cos(5(x-85degrees)) -1.2 compared to y =cos x

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embizze eNotes educator| Certified Educator

Given `y=sqrt(7)cos(5(x-85))-1.2`

Note that for `y=Acos(B(x-h))+k` the amplitude is `A` , the period is `(2pi)/B` in radians, or `360/B` in degrees, the phase shift(horizontal translation) is `h` , and the vertical displacement is `k` .

(1) The amplitude is `sqrt(7)`

(2) The period is `360/5=72`

(3) The phase shift is 85 to the right

(4) The vertical displacement is 1.2 down