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Math Help - trig equation help please

  1. #1
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    trig equation help please

    Hello, I am trying to solve this:

    tan^2(3x)=1 (for values between 0 and 2pi)

    I have broken it down to a 'difference of squares' format:

    (tan3x+1) (tan3x-1)

    I then find the inverse tan of 1 and -1 which gives me 45 degrees and -45 degrees.
    I then divide them by three to give me plus/minus 15.

    I understand that is the first part of the answer, however my text book says the complete answer is +-pi/12 + pi/3 K.
    I understand the pi/3 K part is for repetition, but that is only repeating it every 60 degrees. Looking at graph of tan I see the repetitions would be every 90 degrees ?

    Thanks for any help.
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  2. #2
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    Re: trig equation help please

    Quote Originally Posted by fran1942 View Post
    Hello, I am trying to solve this:

    tan^2(3x)=1 (for values between 0 and 2pi)

    I have broken it down to a 'difference of squares' format:

    (tan3x+1) (tan3x-1)

    I then find the inverse tan of 1 and -1 which gives me 45 degrees and -45 degrees.
    I then divide them by three to give me plus/minus 15.

    I understand that is the first part of the answer, however my text book says the complete answer is +-pi/12 + pi/3 K.
    I understand the pi/3 K part is for repetition, but that is only repeating it every 60 degrees. Looking at graph of tan I see the repetitions would be every 90 degrees ?

    Thanks for any help.
    The period of the tangent function is \displaystyle \begin{align*} \pi \end{align*}, so the solution to the first equation becomes

    \displaystyle \begin{align*} \tan{3x} + 1 &= 0 \\ \tan{3x} &= -1 \\ 3x &= \arctan{(-1)} + \pi k \textrm{ where }k \in \mathbf{Z}  \end{align*}

    What happens when you divide this all by \displaystyle \begin{align*} 3 \end{align*} to find \displaystyle \begin{align*} x \end{align*}?

    Now follow a similar process for \displaystyle \begin{align*} \tan{3x} - 1 = 0 \end{align*}.
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  3. #3
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    Re: trig equation help please

    You could have gone straight from tan^2 3x=1 to saying tan3x=+1 or -1
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