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Trigonometric Equation

  1. Mar 31, 2009 #1
    Hi all,

    I was tutoring someone in Algebra III today and encountered a problem that threw me for a loop.

    (cos x)^4 = cos (x^2)

    Is there a way to solve this algebraically?
     
  2. jcsd
  3. Mar 31, 2009 #2

    Mentallic

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    Hmm... looks so simple, yet it's so not :yuck:

    I wouldn't know of any algebraic methods to solve this.

    y=cos4x is a nice, periodic function like any other standard trig function.

    y=cos(x2) doesn't follow this pattern. As [tex]x \rightarrow \pm \infty[/tex] the period of fluctuations [tex]\rightarrow 0[/tex].

    If there is an algebraic method to solve this - and I highly doubt it - then it can't be pretty.


    Maybe starting with the simple answer x=0 and working from there (I suggest Newton's method :wink:) would be a good start to approach this problem.
     
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