How do you find the amplitude, period, and shift for #y=3 + cot ( (x+pi) / 4)#?

1 Answer
MAXIMILIAN C.
Apr 13, 2018

Amplitude=#a#=#1#
Period =#pi/b#=#pi/4#
Phase Shift =#c#=#-pi# or #-pi# units to the left
Vertical Shift =#d#=3 or 3 units up

Explanation:

Rewrite the equation in standard form of a trig equation:
#y=cot4(x+pi)+3#
Since it is now in the form #y=acotb(x-c)+d# you can use these values to find the features of the equation.
Amplitude =#a#=#1# (in an asymptotal equation such as cotangent, this is also called normal)
Period =#pi/b#=#pi/4#
Phase Shift =#c#=#-pi#
Vertical Shift =#d#=#3#

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