Given the following function:
[tex]\text{ f(x) = cot(x + }\frac{\pi}{6})[/tex]
Use the form a·cot(bx - c) to find the variables used to find the amplitude, period, phase shift and vertical shift.
We get,
a = 1
b = 1
c = -π/6
d = 0
Since the graph of the Cotangent function does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude: None
For the Period:
[tex]\text{ Period = }\frac{\text{ }\pi}{\text{ b}}\text{ = }\frac{\pi}{1}\text{ = }\pi[/tex]
Therefore, the Period is π.
For the Phase Shift:
[tex]\text{ Phase Shift = }\frac{\text{ c}}{\text{ b}}\text{ = }\frac{-\frac{\pi}{6}}{1}\text{ = -}\frac{\pi}{6}[/tex]
Therefore, Phase Shift is -π/6 → π/6 (To the left).
For the Vertical Shift:
Vertical Shift = 0
Plotting the function will be:
