Question 966896
Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5 in quadrant IV
***
cosu=4/5
sinu=-3/5
..
sin(2u)=2sinucosu=2*-3/5*4/5=-24/25
cos(2u)=cos^2(u)-sin^(u)=16/25-9/25=7/25
..
{{{sin(u/2)=sqrt((1-cosu)/2)=sqrt((1-(4/5)/2))=sqrt((1/5)/2)=sqrt(1/10)=sqrt(10)/10}}}
{{{cos(u/2)=-sqrt((1+cosu)/2)=-sqrt((1+(4/5)/2))=-sqrt((9/5)/2)=-sqrt(9/10)=-3/sqrt(10)=-3sqrt(10)/10}}}
..
Check:
cosu=4/5(Q4)
u=323.13
u/2=161.56
2u=646.26
..
sin(u/2)=sin(161.56)=0.3163
exact value as computed=√10/10≈0.3162
..
cos(u/2)=cos(161.56)=-0.9486
exact value as computed=3√10/10≈-0.9486
..
sin(2u)=sin(646.26)=-0.9600
exact value as computed=-24/25=-0.9600
..
cos(2u)=cos(646.26)=.2800
exact value as computed=7/25=0.2800

note: This is a revision of a solution submitted earlier because u was changed to be in quadrant IV  instead of quadrant I