Inverse trignometric function is a function which gives the value of an angle whose one of the trignometric ratios. For example if tan(theta) = 1 Then theta = tan inverse (1) = pi/4
Now as many value of theta can give a given value of trignometric ratio we define their range. In absence of range definition tan inverse(1) can be pi/4, 5pi/4, 9pi/4 etc. So we define range of taninverse from 0 to pi. Si tan inverse(1) will take only a value of pi/4
I hope this clears your concept. I will suggest you that please do some problems and feel free to ask us
Krishna Gopal Singh
B.Tech Chemical Engg
IIT Delhi 2002
Currently doing PhD from IIT Delhi