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Homework Help: Evaluate the value of trigonometry

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data
    evaluate
    sin (π / 62) . sin (15π/62). sin(23π/62). sin(27π/62) . sin(29π/62)


    2. Relevant equations
    trigonometry


    3. The attempt at a solution
    Tried to change it to cos but failed, tried to use 2 sin A sin B identity and failed again

    Thank you very much
     
  2. jcsd
  3. Sep 16, 2010 #2

    Mentallic

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    If you use the property that [tex]sin(x)=cos(\pi/2-x)[/tex] you can get a nice pattern going. See if that helps.
     
  4. Sep 16, 2010 #3
    sin (π / 62) . sin (15π/62). sin(23π/62). sin(27π/62) . sin(29π/62) = cos (30π / 62). cos(16π/62). cos (8π/62). cos(4π/62). cos(2π/62)

    I see no pattern. Is there a nice pattern?
     
  5. Sep 16, 2010 #4

    Mentallic

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    You don't notice a pattern happening? 2,4,8,16,... now you have 30 instead of 32, but you can change it to 32 with another identity.
     
  6. Sep 16, 2010 #5
    I noticed that but lost because of 30 but now I get it from your clue.

    cos (30π / 62) = - cos (32π / 62), then it becomes: - (cos x) . (cos 2x). cos(4x). cos (8x). cos (16x). How to continue that?
     
  7. Sep 16, 2010 #6

    vela

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  8. Sep 16, 2010 #7

    Mentallic

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    harimakenji, I've done stuff like this in an advanced class in high school (in Australia it is called extension 2 mathematics) but usually they first make us prove the given identity as vela has posted and then finally using the formula to evaluate the question that you've been given. Are you sure this question wasn't a continuation from a bigger problem?
     
  9. Sep 16, 2010 #8

    Redbelly98

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    Can you double-check, is the denominator in all those terms supposed to be 62 or 64?
     
  10. Sep 16, 2010 #9

    Mentallic

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    Actually, it works even more nicely being 62 than 64 :wink:
     
  11. Sep 16, 2010 #10
    I also had never seen it before, phew

    The question is just like this, no bigger problem. This is the question for my brother in grade 11.

    It is 62. I've checked the result using calculator and it is very nice result, 1 / 32


    I can solve this question using the link given by vela. I can't do this without all the help here. Thank you very much for the help (vela, mentallic, redbelly98). I really appreciate all the things I got from here. Once again, thank you.
     
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