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Math4Life
Group Title
Use a half–angle identity to find the exact value of sin 105°
 one year ago
 one year ago
Math4Life Group Title
Use a half–angle identity to find the exact value of sin 105°
 one year ago
 one year ago

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baziham Group TitleBest ResponseYou've already chosen the best response.1
i completely answered to you. you must use sin and cos formula and use 105=90+30/2 sin(a+b)=.. sin(2a)=.. cos(2a)=.. try it
 one year ago

Math4Life Group TitleBest ResponseYou've already chosen the best response.0
Ok i'm trying it right now
 one year ago

Math4Life Group TitleBest ResponseYou've already chosen the best response.0
I got 0.260736296 and I have a feeling its not right
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
they want the exact value, not an approximation
 one year ago

Math4Life Group TitleBest ResponseYou've already chosen the best response.0
Yes exact value
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
Hint: Use the half angle formula \[\Large \sin\left(\frac{\theta}{2}\right) = \sqrt{\frac{1\cos(\theta)}{2} }\]
 one year ago

Math4Life Group TitleBest ResponseYou've already chosen the best response.0
I'm so confused
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
notice how 105 = 210/2
 one year ago

Math4Life Group TitleBest ResponseYou've already chosen the best response.0
and 210/2 is 105
 one year ago

Math4Life Group TitleBest ResponseYou've already chosen the best response.0
so are you saying 210 is my answer?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
no, I'm saying the fact that 210 (which is an angle found on the unit circle) divided in half gives you 105
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
so sin(105) = sin(210/2)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
then you would use that formula I gave above
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
I'll get you started Start with this fact \[\Large \sin(105) = \sin\left(\frac{210}{2}\right)\] Then use the formula given previously to get \[\Large \sin(105) = \sqrt{\frac{1\cos(210)}{2} }\] Then use the unit circle to evaluate cos(210) and simplify as much as possible
 one year ago

Math4Life Group TitleBest ResponseYou've already chosen the best response.0
Ok I understand
 one year ago

baziham Group TitleBest ResponseYou've already chosen the best response.1
where \[\cos(210)=\cos(180+30)=\cos(180)\cos(30)\sin(180)\sin(30) \]
 one year ago

baziham Group TitleBest ResponseYou've already chosen the best response.1
answer is \[\sqrt{\frac{ 1\left\{ \cos(180)\cos(30)\sin(180)\sin(30) \right\} }{ 2 }}\]
 one year ago

baziham Group TitleBest ResponseYou've already chosen the best response.1
real answer is: 0.9659258262890682867497431997289
 one year ago

baziham Group TitleBest ResponseYou've already chosen the best response.1
and you can solve above equation and get parametric answer can you do?
 one year ago
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