When calculating the inverse tangent of a degree, the calculator will always give an angle between 90 degrees and –90 degrees. But I want to find the positive value of the negative angle.
Do I add 180 or 360 to the angle?
How do I know if I should add 180 or 360 to the negative angle.
On
$\ tanx=a$
$x=\ arctan(a) + k{\pi}$, $k\in Z$
Period of tangent function is ${\pi}$, it could be added $k{\pi}$, $k\in Z$
Since $f(x)=\tan(x)$ is bijective when $x\in(\dfrac{-{\pi}}{2},\dfrac{{\pi}}{2})$, then, $f(x)=\ arctanx$ is defined as
$f:(\dfrac{-{\pi}}{2},\dfrac{{\pi}}{2}) \rightarrow R$,
I'm not sure I understand what you mean by "positive value of the negative angle"...
A periodic function $f(x)$ has period $p$ if for all integers $n$, $f(x+np)=f(x)$. As Yves pointed out, $\tan x$ has a period of $180^\circ$, meaning that for all real $x$,
$$\tan x=\tan(x\pm180^\circ)=\tan(x\pm360^\circ)=\cdots$$
In particular, if $\tan x=y$ for some given $y$, then $x=\tan^{-1}y+180^\circ n$. By definition of the inverse tangent, $\tan^{-1}y$ is some angle between $-90^\circ$ and $90^\circ$, but it's not the only one that satisfies $\tan x=y$. To get other solutions, you have to add or subtract a multiple of $180^\circ$.
As an example, consider the equation
$$\tan x=1$$
A calculator will tell you that $x=\tan^{-1}1=45^\circ$, but it's also true that $\tan(225^\circ)=\tan(45^\circ+180^\circ)=1$, so $x=225^\circ$ is also a valid solution. Whichever multiple of $180^\circ$ you need to add depends on which domain you expect to find $x$. If $x\in(-90^\circ,90^\circ)$, then $x=45^\circ$; if $x\in(90^\circ,270^\circ)$, then $x=225^\circ$; and so on.