Question

How do you graph and list the amplitude, period, phase shift for `y=tan(x+60)`?

Answer 1

See below.

Explanation:

If we look at a trigonometrical function written in the form:

`y=atan(bx+c)+d`

We know that:

Amplitude = a

Period = `(pi)/b` ( This is the normal period of the function divided by b )

Phase shift = `-c/b`

Vertical shift = d

From example:

`y=tan(x+60)`

Amplitude ( see below)

period `= pi/c` in this case we are using degrees so:

period`=180/1=180^@`

Phase shift`=-c/b=-60/1=60^@`

This is the same as the graph of y = tan(x) translated 60 degrees in the negative x direction

Vertical shift`= d = 0` ( no vertical shift )

Amplitude can not be measured for the tangent function, because as:

as `x->90^@, 270^@`etc ' `color(white)(8888)tan(x)->oo` ( this is undefined )

Graphs: of `y=tan(x) and y= tan(x+60)`