# How do you period and phase shift of the function y=3 tan (4x-pi/3)?

Dec 2, 2016

#### Explanation:

The only good reference that I could find is PDF file Transformations

An equation of the form:

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

The Amplitude is A.

The frequency is $f = \frac{B}{\pi}$

The period is $T = \frac{\pi}{B}$

The phase shift is $\theta = - \frac{C}{B}$

The vertical shift is D

$y = 3 \tan \left(4 x - \frac{\pi}{3}\right)$
$T = \frac{\pi}{4}$
The phase is shift is $\theta = \frac{\pi}{12}$