cos^-1?

For instance

 

cos 23⁰  =  0.9205

 

so

 

cos^-1 0.9205  =  23⁰

 

to get it on the web2.0 calc  press [2nd] then [acos]

 

There is also a toggle button at the bottom that sets the angle to degrees or radians :)

What is actually happening when I use cos^-1?

 

You are getting the angle of that cosine, in degrees. Someday, you will learn how to get an angle in something called "radians".