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Intersections of two graphs (polar coordinates)

  1. Jan 13, 2007 #1
    1. The problem statement, all variables and given/known data

    Find all points of intersection of the two graphs r=sin [tex] \theta [/tex] and r=cos 2 [tex] \theta [/tex]

    3. The attempt at a solution

    sin [tex] \theta [/tex] = cos 2 [tex] \theta [/tex]

    I use the trigonometric identity cos 2x = (cosx)^2 - (sinx)^2 but it doesn't take me any further.
    Last edited by a moderator: Jan 13, 2007
  2. jcsd
  3. Jan 13, 2007 #2


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    Don't forget cos2x = 1 - sin2x

    You should be able to form a quadratic expression in sin(x), which you can solve using the quadratic formula.
  4. Jan 13, 2007 #3
    Thats how you derive the alternate double angle identities, which are meant for a problem like this because they put cos2x in terms of one function
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