Question 752009
given sin theta= -root 7/4 and theta is in quadrant IV, find the exact value of cos theta/2
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{{{cos(x/2)=sqrt((1+cos(x))/2)}}}
{{{sin(x)=-sqrt(7)/4}}}
{{{cos(x)=sqrt(1-sin^2(x))=sqrt(1-7/16)=sqrt(9/16)=3/4}}}
{{{cos(x/2)=-sqrt((1+cos(x))/2)=-sqrt((1+3/4)/2)=-sqrt(7/4)/2)=-sqrt(7/8)}}} ( in Q3 where cos<0)
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Check with calculator:
sinx=-&#8730;7/4 (in Q4)
x=318.49º
x/2=159.30º (in Q3)
cos(x/2)=cos(159.30º)&#8776;-0.9354..
Exact value=-&#8730;(7/8)&#8776;-0.9354..