math - Why are there no asin2() and acos2() functions similar to atan2()? -

From my understanding, atan2 () is present in the programming languages ​​because atan ) can not always determine the right theta because production is limited to -i / 2 to pi / 2.

If this is the case, then the same problem applies to both asin () and acos () , both of which are restricted Then why not asin2 () and acos2 () function?

First of all, note that the syntax is atan (y / x) But atan2 (y, x) , not atan2 (y / x) . This is important because you do not provide additional information while doing division, most importantly the individual symptoms of x and y . If you coordinate the x and y separately, then you know that the angle, including the quartile.

If you have any information about tan (θ) = to y and sqrt (x² + y²) and angle Combines to obtain. It does not matter here that we do divisions ourselves or some hypothetical asin2 function handles it. Everything is always positive, so split logic has a lot of information in the form of different fragments and are of all kinds. (At least one IEEE environment where zero division leads to correctly signed infinity.)

If you enter y coordinates and hypothenuse sqrt (x² + Y²) Then you know the sign of an angle, but you do not know the angle yourself, because you can not distinguish between negative and positive x values. Similarly, if you know the x coordinates and hyperinjues, then you know the cosine of an angle, but you do not know the sign of the value y .

Therefore asin2 and acos2 are not mathematically viable, not at least in a clear way. If you had any kind of signal encoded in the hyperense, things might be different, but I can not think of a situation where such signs would arise naturally.