Question 966988
{{{cos(u)=4/5}}}
{{{cos^2(u)+sin^2(u)=1}}}
{{{16/25+sin^2(u)=1}}}
{{{sin^2(u)=9/25}}}
{{{sin(u)=0 +- 3/5}}}
Since it's Q4, {{{sin(u)=-3/5}}}
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{{{sin(2u)=2sin(u)cos(u)}}}
{{{sin(2u)=2(-3/5)(4/5)}}}
{{{sin(2u)=-24/25}}}
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{{{cos(2u)=cos^2(u)-sin^2(u)}}}
{{{cos(2u)=(16/25)-(9/25)}}}
{{{cos(2u)=7/25}}}
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{{{sin(u/2)=0 +- sqrt((1-cos(u))/2)}}}
{{{sin(u/2)=0 +- sqrt((1-4/5)/2)}}}
{{{sin(u/2)=0 +- sqrt((1/5)/2)}}}
{{{sin(u/2)=0 +- sqrt(1/10)}}}
{{{sin(u/2)=0 +- sqrt(10)/10}}}
Now since {{{u}}} is in Q4, {{{u/2}}} would be in Q2, where sine is positive.
{{{sin(u/2)=sqrt(10)/10}}}
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{{{cos(u/2)=0 +- sqrt((1+cos(u))/2)}}}
{{{cos(u/2)=0 +- sqrt((1+4/5)/2)}}}
{{{cos(u/2)=0 +- sqrt((9/5)/2)}}}
{{{cos(u/2)=0 +- 3/sqrt(10))}}}
{{{cos(u/2)=0 +- (3/10)sqrt(10) )}}}
Again since {{{u}}} is in Q4, {{{u/2}}} would be in Q2, where cosine is negative.
{{{cos(u/2)=-(3/10)sqrt(10)}}}