SOLUTION: Need help!!!! Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5. Now I know to make a triangle a^2+b^2=c^2. Then you get the missing line which is 3. Fr

Algebra ->  Trigonometry-basics -> SOLUTION: Need help!!!! Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5. Now I know to make a triangle a^2+b^2=c^2. Then you get the missing line which is 3. Fr      Log On


   

Question 966896: Need help!!!! Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5. Now I know to make a triangle a^2+b^2=c^2. Then you get the missing line which is 3. From there sin(2u) and cos(2u) use the double Angle formula and get sin(2u)=-24/25 and cos(2u)=7/25. I even get how to solve the sin and cos of u/2 by using the half angle formulas but what I'm confused on is the positive and negative answers. I thought sin u/2=-√(10)/10 and cos u/2= 3(√(10)/10) but it's actually sin u/2=+√(10)/10 and cos u/2= -3(√(10)/10). I'm so confused. Shouldn't sin u/2 be - because it is in the fourth quadrant???
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5 in quadrant IV
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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
..


..
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