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

Apr 13, 2018

Amplitude=$a$=$1$
Period =$\frac{\pi}{b}$=$\frac{\pi}{4}$
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:
$y = \cot 4 \left(x + \pi\right) + 3$
Since it is now in the form $y = a \cot b \left(x - c\right) + d$ 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 =$\frac{\pi}{b}$=$\frac{\pi}{4}$
Phase Shift =$c$=$- \pi$
Vertical Shift =$d$=$3$