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Trig Function

  1. Nov 2, 2005 #1
    I am stuck on this problem:

    It tells me to use the Half-Angle Formulas to find the exact value of the trig function.

    sec((15*pi)/8)

    I know I should convert that into the cos function and when I do I get:

    cos(8/(15*pi))

    But now I need to find cos(alpha/2) to be able to use the Half-Angle formula. I think what I can do is multiply it by 2 and then that would be my alpha, then I could just plug it in right? So then I would have:

    cos((16/(15*pi))/2)

    I am not sure if this is right so far or if I am even on the right track.
     
  2. jcsd
  3. Nov 2, 2005 #2

    verty

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    Homework Helper

    As far as I can see:

    sec(15*pi/8)
    = sec(2pi - pi/8)
    = sec(pi/8)
     
  4. Nov 2, 2005 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    NO!!! sec x= 1/(cos(x)) not cos(1/x)!
    Use the Half-Angle Formula alright but to go the other way!
    sec(15pi/8)= 1/cos(15pi/8) so you just need to find cos(15pi/8)
    That is [tex]cos(15pi/8)= \sqrt{\frac{1}{2}(1+ cos(15pi/4))}[/tex].
    cos(15pi/4) is easy.
     
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