yes, amplitude is five and period is 3 pi
when x = 0:
y = 5 cos (-pi/6) = 5 (.866)
that is not a max or a min or and x intercept
However there is always a reflection about the points where the argument of the cos function is zero because cos -z = cos z
that is when
(4/6)x = pi/6
or x = pi/4 which is 45 degrees
of course every time that argument increases or decreases by 2 pi (which is x increases or decreases by 3 pi as you said) you have another max and symmetry
Yes, (pi/6)/(2/3) = pi/4 = phase shift
see:
http://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html
Consider the function
f(x)=-5cos((2/3)x-(pi/6))
a). Is there a reflection? Does the graph start at a maximum, a minimum, or an x-intercept?
For Amplitude I got 5
For Period I got 3pi
And for Phase shift I got 3pi/12 or => pi/4
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