Question

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

Answer 1

Please see the explanation.

Explanation:

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

An equation of the form:

`y = (A)tan(Bx + C) + D`

The Amplitude is A.

The frequency is `f = B/pi`

The period is `T = (pi)/B`

The phase shift is `theta = -C/B`

The vertical shift is D

For your function:

`y = 3 tan(4x - pi/3)`

You did not ask for the amplitude or vertical shift but they are 3 and 0, respectively.

The period is:

`T = pi/4`

The phase is shift is `theta = pi/12`