Trig Identity Problem

  1. I have been set an exercise from my text book to do for homework but I am having some problems on one of the questions, I havn't encountered any of this type before and I am quite stumped.

    "Eliminate [tex]\theta[/tex] from equations [tex]x=2+\csc\theta[/tex] and [tex]y=\frac{1}{4}\tan\theta[/tex]"

    So I am guessing I start off with x=y but then... :confused:
  2. jcsd
  3. Fermat

    Fermat 876
    Homework Helper

    start off by getting separate expressions for cscθ and tanθ from each of your two eqns.
    Now you have to eliminate θ.
    Can you do it from there ?
  4. So for the first one would it goto,
    [tex]2+\frac{1}{\sin\theta}=3+\cot\theta[/tex] Then try eliminate theta from there?
  5. Fermat

    Fermat 876
    Homework Helper

    not quite.
    get two separate expressions. One for cscθ and one for tanθ.
    Then find a trig identity involving the trig functions. You will have to manipulate the functions to get the identity.
  6. I'm not sure what you are saying, get an expression for each equation so for the first one would become [tex]2+\cot\theta[/tex] and the second one [tex]\frac{1}{4}\csc\theta-\frac{1}{4}[/tex] then put them equal to each other and try solve it?
    I would appreciate it if you could show me the first step in tex form
    Last edited: Oct 9, 2005
  7. Fermat

    Fermat 876
    Homework Helper

    hang on a minute.
  8. Fermat

    Fermat 876
    Homework Helper

    x = 2 + cscθ
    y = ¼tanθ

    cscθ = x - 2
    tanθ = 4y

    1 + tan²θ = sec²θ
  9. Ahhh, it all becomes clear. Thanks a lot for the help It seems so easy now.
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