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Exact value of sin 65

  1. Nov 12, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the exact value of sin 65o

    2. Relevant equations
    Trigonometry Identities

    3. The attempt at a solution
    I tried using sin 3x = 3 sin x - 4 sin3x but ended with nasty algebra.

    sin (3 . 65o) = 3 sin 65 - 4 sin3 65o
    sin (195o) = 3 sin 65 - 4 sin3 65o
    sin (180o+15o) = 3 sin 65 - 4 sin3 65o
    - sin (15o) = 3 sin 65 - 4 sin3 65o ; let sin 65o = x
    (√2 - √6) / 4 = 3x - 4x3

    Can't solve for x

    Thanks
     
  2. jcsd
  3. Nov 12, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    There is a formula for analytic solutions for the last equation. Using that is probably easier than finding different trigonometric identities.

    You could try to establish a value for sin(10o) first I guess.
     
  4. Nov 12, 2015 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Somebody has published (on the internet) a list of exact formulas involving roots and the like, for the sine function for all angles in 1 degree increments from 1 degree to 90 degrees. The work includes proofs of all the results. (It was done as a retirement project by an ex-professor of mathematics.) For more details, see

    http://www.intmath.com/blog/mathematics/how-do-you-find-exact-values-for-the-sine-of-all-angles-6212
     
    Last edited: Nov 12, 2015
  5. Nov 14, 2015 #4
    Thanks for all the help
     
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