SOLUTION: Sinusoidal Functions Without graphing, determine the amplitude, period, equation of the axis, phase shift, domain, and range of the function y=20 cos(9x-81°)-2

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Question 1140741: Sinusoidal Functions
Without graphing, determine the amplitude, period, equation of the axis, phase shift, domain, and range of the function y=20 cos(9x-81°)-2
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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

a is the amplitude
360/b degrees is the period
c is the positive phase shift (that is, x-45 means shift 45 degrees to the right; x+60 (= x-(-60)) means shift 60 degrees to the left)
d is the vertical shift

Put your function in that form by factoring out the coefficient of x:

y+=+20%2Acos%289%28x-9%29%29-2

amplitude: a = 20
period: 360/b = 360/9 = 40 degrees
phase shift: c = 9 degrees to the right
vertical shift: d = -2, which means the axis (center line) is y=-2
domain: all reals
range: plus or minus 20 from the center line of -2, so -22 to +18