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

Question

43950 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-18T14:46:32

See below.

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)#

enter image source here