Question 349082
(For reasons I do not know, Algebra.com's formula software does not do theta, So I will be using alpha, {{{alpha}}}, instead.<br>
The general formula is {{{sin(alpha/2) = 0 +- sqrt((1-cos(alpha))/2)}}}
(The zero in front is due to another limitation of Algebra.com's software.)
Since {{{alpha}}} is between 270 and 360, sin is negative so we will use:
{{{sin(alpha/2) = - sqrt((1-cos(alpha))/2)}}}
Replacing {{{cos(alpha)}}} with 2/3 we get:
{{{sin(alpha/2) = - sqrt((1-(2/3))/2)}}}
Simplifying:
{{{sin(alpha/2) = - sqrt((3/3-(2/3))/2)}}}
{{{sin(alpha/2) = - sqrt((1/3)/2)}}}
{{{sin(alpha/2) = - sqrt(1/6)}}}
{{{sin(alpha/2) = - sqrt((1/6)(6/6))}}}
{{{sin(alpha/2) = - sqrt(6/36)}}}
{{{sin(alpha/2) = - sqrt(6)/sqrt(36)}}}
{{{sin(alpha/2) = - sqrt(6)/6}}}
which is the simplified, exact value for {{{sin(alpha/2)}}}.