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

Question 966988: Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5 where 3pi/2< u <2pi. 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 Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Since it's Q4,
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Now since is in Q4, would be in Q2, where sine is positive.

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Again since is in Q4, would be in Q2, where cosine is negative.

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