I think you entered a number wrong, since your calculator otherwise got the right answer. None of these functions are going into particularly dangerous areas for precision. When I round every step to 6 figures on my calculator, I still get 24.9999
Heck, rounding every step to 2 figures still gets me .41 radians which is 23.5 degrees.
I...how? That's the same on most of the numbers, but even more precision on one of them.
Here's my calculator, with exactly three decimal places:
25->rad: .436
sin(.436): .422
cos(.422): .912
tan(.912): 1.292
atan(1.292): .912
acos(.912): .422
asin(.422): .435
.435->deg: 24.924
Where does your calculator start to diverge, that you end up with an answer like 9?
And I got the same result as Aardwolf that the Sinclair emulator returns .434, only a tenth of a degree off.
Edit: Oh wait, you're using a calculator set to degrees. That's a totally different problem, because it makes the 0-1 output from sin and cos become an extremely small fraction of a circle. It works as a type of precision test, but it's not at all the same thing you'd try on the Sinclair that only does radians. It still doesn't explain your original memory.
Side note: Even in degrees mode, the answer for 6 digits is kind of an outlier. If you use 5 or fewer digits the calculation crashes. 7 digits gets you 24.9. It boils down to just acos(cos( [about half a degree] )), and the other operations don't really matter.
Heck, rounding every step to 2 figures still gets me .41 radians which is 23.5 degrees.