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Math Help - Trig Problem

  1. #1
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    Trig Problem

    Hi there.

    Ive had a good look on the forum and cant seem to find anything to help me in this situation, just cant seem to figure this one out, here goes anyway

    \tan 2x = \frac{1}{3} where \tan x = -3 \pm\sqrt{10}

    Any help with this would be really appreciated, ive been looking at it hours now and its just not making sence to me.

    Ive had a look at double angle formula, but they dont seem to relate to each other.

    Thanks very much
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  2. #2
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    Quote Originally Posted by farso View Post
    Hi there.

    Ive had a good look on the forum and cant seem to find anything to help me in this situation, just cant seem to figure this one out, here goes anyway

    \tan 2x = \frac{1}{3} where \tan x = -3 \pm\sqrt{10}

    Any help with this would be really appreciated, ive been looking at it hours now and its just not making sence to me.

    Ive had a look at double angle formula, but they dont seem to relate to each other.

    Thanks very much
    Double angle formula: \tan(2x) = \frac{2 \tan x}{1 - \tan^2 x}.

    Therefore:

    \frac{1}{3} = \frac{2 \tan x}{1 - \tan^2 x}

     \Rightarrow \frac{1}{3} (1 - \tan^2 x) = 2 \tan x

     \Rightarrow 1 - \tan^2 x = 6 \tan x

    \Rightarrow \tan^2 x + 6 \tan x - 1 = 0.

    This is a quadratic equation in tan x. Solve it using the quadratic formula:

    \tan x = -3 \pm \sqrt{10}.
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  3. #3
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    Mar 2008
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    Thanks very much! I can see exactly how i was ment to do that now the answer is in front of me!

    Always the way isnt it?

    Should be good for next time though, thanks!
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