# How do you find the amplitude, period and phase shift for y=1/4tan2(theta+30^circ)+3?

Mar 18, 2018

$\text{Amplitude " = "None}$, Function tan x does not have amplitude.

$\text{Period} = P = \frac{\pi}{|} B | = \frac{\pi}{2}$

$\text{Phase Shift } = \frac{- C}{B} = - {60}^{\circ} / 2 = - \frac{\pi}{3 \cdot 2} = - \frac{\pi}{6}$

$\text{Vertical Shift } = D = 3$

#### Explanation:

Standard Form $y = A \tan \left(B x - C\right) + D$

Given : y = (1/4) tan (2(theta + 30^@) + 3

$\text{Amplitude " = "None}$, Function tan x does not have amplitude.

$\text{Period} = P = \frac{\pi}{|} B | = \frac{\pi}{2}$

$\text{Phase Shift } = \frac{- C}{B} = - {60}^{\circ} / 2 = - \frac{\pi}{3 \cdot 2} = - \frac{\pi}{6}$

$\text{Vertical Shift } = D = 3$

graph{(1/4) tan (2x + (pi/3)) + 3 [-10, 10, -5, 5]}