Question 669253
what is the exact value of sin(11pi/12)
<pre>
There are 6 different ways we can go about this 
since {{{11pi/12}}} can be written in as the sum or difference
of special angles in these 6 ways:

{{{11pi/12) = {{{7pi/4-5pi/6}}} = {{{7pi/4-5pi/6}}} = {{{5pi/4-pi/3}}} = {{{pi/6+3pi/4}}} = {{{2pi/3+pi/4}}} = {{{5pi/3-3pi/4}}} = {{{7pi/6-pi/4}}}

I'll pick one arbitrarily, say

{{{11pi/12}}} = {{{2pi/3+pi/4}}}

{{{sin(11pi/12)}}} = {{{sin(2pi/3+pi/4)}}} 

We use the formula:

{{{sin(alpha+beta)=sin(alpha)cos(beta)+cos(alpha)sin(beta)}}}

{{{sin(11pi/12)}}} = {{{sin(2pi/3+pi/4)}}} = {{{sin(2pi/3)cos(pi/4)+cos(2pi/3)sin(pi/4)}}} = 
{{{(sqrt(3)/2)(sqrt(2)/2)+(-1/2)(sqrt(2)/2)}}} = {{{sqrt(6)/4-sqrt(2)/4}}} = {{{(sqrt(6)-sqrt(2))/4}}} 

Edwin</pre>