Question 987163
<pre>
{{{arcsin(sin(-19pi/6)^"")}}}

Add 2<font face="symbol">p</font>n to the angle.

{{{arcsin(sin(-19pi/6+2pi*n)^"")}}}

Set the angle between 0 and 2<font face="symbol">p</font> 

{{{0<= -19pi/6+2pi*n < 2pi}}}

Divide through by <font face="symbol">p</font>

{{{0<=-19/6+2n < 2}}}

Multiply through by 6

{{{0<=-19+12n < 12}}}

Add 19 to both sides

{{{19<=12n < 31}}}

Divide through by 12

{{{1.583<=n<2.583}}}

So n = 2

{{{arcsin(sin(-19pi/6+2pi*2)^"")}}}

{{{arcsin(sin(-19pi/6+4pi)^"")}}}

{{{arcsin(sin(-19pi/6+24pi/6)^"")}}}

{{{arcsin(sin(5pi/6)^"")}}}

{{{arcsin(1/2)}}}

{{{pi/6}}}

Edwin</pre>