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

Dec 18, 2017

See below.

#### Explanation:

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

$y = a \tan \left(b x + c\right) + d$

We know that:

Amplitude = a

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

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

Vertical shift = d

From example:

$y = \tan \left(x + 60\right)$

Amplitude ( see below)

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

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

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

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 $x \to {90}^{\circ} , {270}^{\circ}$etc ' $\textcolor{w h i t e}{8888} \tan \left(x\right) \to \infty$ ( this is undefined )

Graphs: of $y = \tan \left(x\right) \mathmr{and} y = \tan \left(x + 60\right)$