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Trig theta Question

  1. May 27, 2008 #1
    [SOLVED] Trig Question

    1. The problem statement, all variables and given/known data
    Let's say I have [tex]tan(2\theta) = cot(\phi)[/tex] I'm not quite sure how to simplify it (I want to solve for theta) I could say [tex]tan(2\theta) = 1 / tan(\phi)[/tex]
    [tex]2\theta = atan( 1 / tan(\phi) ) [/tex] but then I'm not sure what to do after that.
    Do I take the atan of 1 and [tex]tan(\phi)[/tex]?

    I know another method to find it is to say [tex]cot(\phi) = \pi/2 - tan(\phi)[/tex] but I don't understand that either because [tex]2\theta = atan( \pi/2 - tan\phi ) != \pi/2 -\phi [/tex] (not exactly at least)

    The answer as far as I know is supposed to be [tex]2\theta = \pi/2 -\phi [/tex]
    Last edited: May 27, 2008
  2. jcsd
  3. May 27, 2008 #2


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    Homework Helper

    Remember that that the tangent of angle is the cotangent of its complement and go from that definition.

    OR you could say that

    [tex]tan(2\theta) = cot(\phi) \Rightarrow \frac{2tan\theta}{1-tan^2\theta}=\frac{1}{tan\phi}[/tex]

    and solve from there.

    Two ways really, one is easier than the other though.
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