anonymous
  • anonymous
Find an exact value. cos(pi/12)
Mathematics
katieb
  • katieb
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welshfella
  • welshfella
i think we can use cos 2x = 2cos^2x - 1 cos (pi/6) = 2 cos^ (pi/12) - 1 cos pi/6 = sqrt3/2
anonymous
  • anonymous
they want you to use the half angle formula \[\cos \frac{ x }{ 2 }= \pm \sqrt{\frac{ 1+cosx }{ 2 }}\]
welshfella
  • welshfella
oh ok well just plug cos x ( in this case cos pi/6) into the firmula and work it out

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anonymous
  • anonymous
when I do I don't get the right answer
anonymous
  • anonymous
The answer options are (sqrt6+sqrt2)/4 (-sqrt6+sqrt2)/4 (sqrt6-sqrt2)/4 (-sqrt6-sqrt2)/4
welshfella
  • welshfella
yes its an awkward one to work out
anonymous
  • anonymous
How would you work it out?
welshfella
  • welshfella
= sqrt [( 1 + sqrt3/2)/ 2]
anonymous
  • anonymous
How do you get from that to one of the answers? I dont understand how you get a sqrt 6 out of any of that
welshfella
  • welshfella
i simplified that to (1/2)( sqrt(2 + sqrt3))
welshfella
  • welshfella
i agree I think those answers are wrong.
welshfella
  • welshfella
because if you go on the calculator cos pi/12 = 0.9659 and my answers comes to the same value
welshfella
  • welshfella
oh hold on (sqrt6+sqrt2)/4 comes to 0.9659 as well so that one is right
welshfella
  • welshfella
- also the negative of that is another solution
welshfella
  • welshfella
I'm not sure how they got to that ...

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