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

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Answer 1 · 2017-12-18T14:46:32

See below.

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

$y = a tan (b x + c) + d$ $y=atan(bx+c)+d$

We know that:

Amplitude = a

Period = $\frac{π}{b}$ $(pi)/b$ ( This is the normal period of the function divided by b )

Phase shift = $- \frac{c}{b}$ $-c/b$

Vertical shift = d

From example:

$y = tan (x + 60)$ $y=tan(x+60)$

Amplitude ( see below)

period $= \frac{π}{c}$ $= pi/c$ in this case we are using degrees so:

period $= \frac{180}{1} = 180^{\circ}$ $=180/1=180^@$

Phase shift $= - \frac{c}{b} = - \frac{60}{1} = 60^{\circ}$ $=-c/b=-60/1=60^@$

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

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

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

as $x \to 90^{\circ}, 270^{\circ}$ $x->90^@, 270^@$ etc ' $8888 tan (x) \to \infty$ $color(white)(8888)tan(x)->oo$ ( this is undefined )

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

enter image source here

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