## 2230 Reputation

4 years, 277 days

## Some experiments...

to avoid complex explanations with branched solutions.

In the real domain with

`plots:-inequal(a < cos(x), x = -6 .. 6, a = -3 .. 3)`

solutions are located here:

Applying now arccos to both sides of the relation and flipping < to > because of the negative slope of arccos (and inverting the axes):

`plots:-inequal(arccos(cos(x)) < arccos(a), a = -3 .. 3, x = -6 .. 6)`

gives a better view on all solutions for a given a. The simple solution you have derived by hand looks probably something like this

```map(arccos, cos(x) < a);
simplify(%, symbolic);```

`plots:-inequal(x < arccos(a), a = -3 .. 3, x = -6 .. 6)`

This depicts the problem with your apparently simple relation to solve: You have to restrict this not only to a but also to x.

`plots:-inequal(abs(x) < arccos(a), a = -3 .. 3, x = -6 .. 6)`

The plotted solutions above do not reflect the periodicy of all solutions. I think that's the reason why you got the message about potentially lost solutions. Why Maple does not provide at least one of these two solutions

`solve(abs(x) < arccos(a), x)`

is up to someone else to explain

## Y(Y)?...

before fsolve you do

`W := unapply(W(Y), Y)`

With 2023 I get

Maple can formally differentiate W but not evaluate the result at 0

Do you really want to "make functions" with unapply that way?

## An unsatisfactory workarround...

Unfortunately, the 3d workspace is not working well with newer features and functionalities (like the CAD toolbox in your case).

A workaround, that hopefully will not become good practice, is to copy the content of the subsystem and paste it to the main subsystem canvas. The subsystem from the CAD toolbox can be binned or later, after finished assembly, replace the pasted components.