Question 964583
If cos&#952; = -2/3, and 450 degrees < &#952; < 540 degrees, find: 
A) Exact value of cos(1/2)&#952;
B) Exact value of tan(2&#952;)
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{{{cos(x/2)=-sqrt((1+cosx)/2)=-sqrt((1-2/3)/2)=-sqrt(1/6)}}}
{{{sinx=sqrt(1-cos^2(x))=sqrt(1-4/9)=sqrt(5/9)=sqrt(5)/3}}}
..   
sin(2x)=2sinxcosx=2sqrt(5)/3*-2/3=-(4&#8730;5)/9
cos(2x)=cos^2(x)-sin^2(x)=4/9-5/9=-1/9
tan(2x)=sin(2x)/cos(2x)=4&#8730;5
..
check:
cosx=-2/3
x=491.81&#730;
2x=983.62&#730;
x/2=245.91
cos(x/2)&#8776;cos(245.91)&#8776;-0.4082
exact value as computed above=&#8730;(1/6)&#8776;-0.4082
tan(2x)=tan(983.62)&#8776;8.94
exact value as computed above=4&#8730;5&#8776;8.94