Question 1171878
<pre>
The radian measure for 0°, 90°, 180°, 270°, and 360° are

0, &pi;/2, &pi;, 3&pi;/2, and 2&pi; which have approximate decimal values:

0, 1.57, 3.14, 2.36, and 6.28. 
</pre>Find the reference angle for {{{theta= -22pi/9}}}<pre>
We can add any integer, positive or negative times {{{2pi}}} and
have an angle coterminal with {{{theta= -22pi/9}}}.

First we find the smallest coterminal angle which is between 0 and 2&pi;,

{{{0<=-22pi/9+2pi*n<2pi}}}

Clear of fractions by multiplying through by 9

{{{0<=-22pi+18pi*n<18pi}}}

Divide all three sides by 2&pi;

{{{0<=-11+9*n<9}}}

Add 11 to all three sides:

{{{11<=9*n<20}}}

Divide through by 9

{{{11/9<=n<20/9}}}

{{{"1.22..."<="2.22..."}}}

Since n must be an integer,

{{{n=2}}}

Substitute n=2 in 

{{{-22pi/9+2pi*n}}}

{{{-22pi/9+2pi*2}}}

{{{-22pi/9+4pi}}}

{{{-22pi/9+36pi/9}}}

{{{14pi/9}}}

This is approximately 4.89 which puts it in QIV

So to get the reference angle, we subtract from 2&pi;:

{{{2pi-14pi/9}}}

{{{18pi/9-14pi/9}}}

{{{4pi/9}}}  <-- reference angle.

Edwin</pre>