# How do you determine period, amplitude and phase shift for y = 1 + cot ( 3x + pi/2 ) ?

Jul 13, 2018

As below.

#### Explanation:

Standard form of a cotangent function is $y = A \cot \left(B x - C\right) + D$

$\text{Given } y = 1 + \cot \left(3 x + \frac{\pi}{2}\right)$

$A = 1 , B = 3 , C = - \frac{\pi}{2} , D = 1$

#Amplitude = |A| = " NONE" for cotangent function

$\text{Period } = \frac{\pi}{|} B | = \frac{\pi}{3}$

$\text{Phase Shift "= -C / B = (pi/2) / 3 = pi/6, color(red)(" "pi/6 " to the RIGHT}$

$\text{Vertical Shift } = D = 1$ graph{cot (3x + pi/2) + 1 [-10, 10, -5, 5]}