OK, so posted some Prime results on the following forum:

For those that have an actual Prime calculator....

This refers to the emulator with firmware rev. 5106. From the link above it is evident that the first release of the actual Prime will give the same result.

Here's the screen capture again:

So what's my problem with this?

OK, apart from the "+-" and "--", quite a bit.

First, let's look at ACOS(2):

The "radian mode" answer is correct:

This agrees with the symbolic radian mode answer of the Prime.

Numerically:

Now:

So:

But now let's look at the "degrees mode" answer. In the complex domain it is more common to continue with radian angles even when settings are in degrees. However, it is possible to do it in degrees, but it must be done carefully and correctly.

Let's look at the HP Prime approach:

Oh, oh, we are now subtracting a radian angle from degrees!!!

And that's how the Prime gets it's incorrect answer!!

The right way:

Similarly the Prime gets the wrong answer for ACOS(-2) in degrees mode.