1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Aime 2008 Ii 8

  1. May 20, 2008 #1
    [SOLVED] Aime 2008 Ii 8

    1. The problem statement, all variables and given/known data
    Let [itex]a = \pi/2008[/itex]. Find the smallest positive integer n such that
    [tex]2[\cos(a)\sin(a)+\cos(4a)\sin(2a)+\cos(9a)\sin(3a)+\cdots+\cos(n^2a)\sin(na)] [/tex]
    is an integer.

    2. Relevant equations
    [tex]\cos(a+b) = \cos a \cos b- \sin a \sin b[/tex]

    [tex]\sin (a+b) = \sin a \cos b + \sin b \cos a[/tex]

    3. The attempt at a solution
    Can someone give me a hint please? This should only require high school math. I am not sure if the identities above are useful here or if there is a totally different method needed.
  2. jcsd
  3. May 20, 2008 #2
    It's an AIME trig problem, which often means you have to play around with it and hope things end up canceling. You have a product which is difficult to sum, so try changing the product into a sum using the sum to product identities:

  4. May 20, 2008 #3
    very nice
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook