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

Algebra ->  Trigonometry-basics -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28u%29=4%2F5
cos%5E2%28u%29%2Bsin%5E2%28u%29=1
16%2F25%2Bsin%5E2%28u%29=1
sin%5E2%28u%29=9%2F25
sin%28u%29=0+%2B-+3%2F5
Since it's Q4, sin%28u%29=-3%2F5
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sin%282u%29=2sin%28u%29cos%28u%29
sin%282u%29=2%28-3%2F5%29%284%2F5%29
sin%282u%29=-24%2F25
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cos%282u%29=cos%5E2%28u%29-sin%5E2%28u%29
cos%282u%29=%2816%2F25%29-%289%2F25%29
cos%282u%29=7%2F25
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sin%28u%2F2%29=0+%2B-+sqrt%28%281-cos%28u%29%29%2F2%29
sin%28u%2F2%29=0+%2B-+sqrt%28%281-4%2F5%29%2F2%29
sin%28u%2F2%29=0+%2B-+sqrt%28%281%2F5%29%2F2%29
sin%28u%2F2%29=0+%2B-+sqrt%281%2F10%29
sin%28u%2F2%29=0+%2B-+sqrt%2810%29%2F10
Now since u is in Q4, u%2F2 would be in Q2, where sine is positive.
sin%28u%2F2%29=sqrt%2810%29%2F10
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cos%28u%2F2%29=0+%2B-+sqrt%28%281%2Bcos%28u%29%29%2F2%29
cos%28u%2F2%29=0+%2B-+sqrt%28%281%2B4%2F5%29%2F2%29
cos%28u%2F2%29=0+%2B-+sqrt%28%289%2F5%29%2F2%29
cos%28u%2F2%29=0+%2B-+3%2Fsqrt%2810%29%29
cos%28u%2F2%29=0+%2B-+%283%2F10%29sqrt%2810%29+%29
Again since u is in Q4, u%2F2 would be in Q2, where cosine is negative.
cos%28u%2F2%29=-%283%2F10%29sqrt%2810%29