Question 909017
<pre>
You can't go by what the calculator gives for sin<sup>-1</sup> unless
you want only the answer between {{{-pi/2}}} and {{{"" + pi/2}}}.

Also it's better not to round off until the end.

What you do is fisrt find sin<sup>-1</sup> of POSITIVE 0.2 which will
give the QI answer of .2013579209, which is not a solution, but only
the reference angle in radians.  

First let's find the positive values, then we'll find the negative values.

We know that the sine is negative only in QIII and QIV,  So to get the 
first positive QIII answer we add {{{pi}}} to the reference angle to get
3.342950574.  To get the first QIV answer we subtract the reference angle
from {{{2pi}}} and get 6.081827386.

So the first two positive solutions are 3.342950574 and 6.081827386

Now we begin adding {{{2pi}}} to each of those and get as many answers
as we can that don't exceed {{{5pi}}} which is 15.70796327.

Adding {{{2pi}}} to 3.342950574 and 6.081827386 gives

                    9.626135882 and 12.36501269

Adding {{{2pi}}} to those gives

                   15.90932119 and 18.648198, but both are too large.

So all the positive solutions are

3.342950574, 6.081827386, 9.626135882 and 12.36501269.

Now let's find the negative solutions.

We go bact to the first two positive solutions, 3.342950574 and 6.081827386

Now we begin subtracting {{{2pi}}} from each of those and get as many 
negative solutions as we can that don't go below {{{-pi}}} which is 
-3.141592654.

Subtracting {{{2pi}}} from 3.342950574 and 6.081827386 gives
                        -2.940234733 and -.2013579208

Subtracting {{{2pi}}} from those gives

                       -9.22342004 and -6.484543228 both too small.

So all the solutions are, smallest to largest:

       -2.94, -0.20, 3.34, 6.08, 9.63, 12.37 
                           
Edwin</pre>