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Cos2v= cos v

  1. Oct 12, 2004 #1
    How do I solve these two:

    cos 2v = cos v

    sin 2v = sin v
     
  2. jcsd
  3. Oct 12, 2004 #2

    plover

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    Homework Helper

    Double angle formulas, e.g. sin 2x = 2(sin x)(cos x)
    So your second equation becomes:
    2(sin x)(cos x) = sin x
     
  4. Oct 12, 2004 #3
    cos2v=2(cosv)^2-1
    t=cosv and solve equation.
    The second I remmember you already asked and were properly answered by matt and mods, so why "repeat" it ?:confused:

    [dont forget to choose only t's in the range [-1,1] only]
     
  5. Oct 12, 2004 #4

    wm

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    Does it go like this?

    (1) cosv = cos2v = cos( v + v) = cosv cos v - sinv sinv

    = cosv [cos v] - [sinv sinv] = cosv[ 1] - [0] if it is to equal cosv, as given.

    Therefore need: [cosv] = 1 and [sinv] = 0; so v = 0.

    [PS: Your teacher may prefer Motifs' suggestion where you solve a standard quadratic equation.]

    (2) is similar, but more interesting. Good luck.
     
    Last edited: Oct 12, 2004
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