How to find out a trigonometric inverse of any given number ? Eg- sin^-1(0.1308)

You have to use sine table for calculating arc sine value, 
Step 1: In a sine table, locate the number whose ${\sin }^{-1}$ you want to find out.
Step 2: The required value is = $\mathrm{corresponding} \mathrm{column} +\frac{\mathrm{corresponding} \mathrm{row}}{10}$

Note:- The value given by the table is in degrees and not in radians.

So the value of ${\sin }^{-1}(0.1308)=7.{51}^0$