How do I work with arcsin, arccos, and arctan in trigonometry for precalc?

Question

wolf1728 · Answer

Basically, those are used in all branches of math - not just precalc.

You know for example, the tangent of 60° = 1.7320508076

but let's suppose you are trying to determine an angle.
For example you have an angle whose opposite side is 1.732 and the adjacent side is 1.  What is the angle?  
Since you are dealing with an opposite side divided by an adjacent side, you know it involves a tangent.  
Since you want to know an angle, then you would look up what angle has the tangent value of 1.732.  Or another way to put this, what is the arc tangent of 1.732?  
and the answer is 60°