Well, since you are only providing a single number to the program......
Which value is NUM? Perhaps cosine?
I will go with that conjecture .... that being said ...
ArcCosine = ArcTangent √(1 - cosine²) cosine
Of course this will only return the angles where:
0 < ArcCosine < pi
So.....
If that is what you are asking, then as long as you are not expecting the Q-III and Q-IV results you should be fine.
Does that make sense?
But then again it looks like you have a decent handle on Trig already....