SOLUTION: Hello, I need help solving this trigonometric equation. I recently posted this, but I forgot to write it as an equation. The question is: solve the following question for &#952

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Question 1092909: Hello, I need help solving this trigonometric equation. I recently posted this, but I forgot to write it as an equation.
The question is: solve the following question for θ. Unless otherwise specified, give all solutions as exact radian measurements such that 0 ≤ θ < 2pi.
1. (3tan 3θ)^2 -27=0
I appreciate any time and effort that you put into solving this. Thank you in advance for your help!
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
I'll take a stab at it




Take the square root of both sides

-----------------------------
Since
and, also

------------------------------


and also:


-----------------------
Get another opinion on this
( unless you know my solution is correct )



Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
 - 27 = 0  ====>

 = 27 ====>

 = 27  ====>  divide by 9 each side  ====>

 = 3  ====>

 = +/- .


1)   =   ====>   =   or    or    or    or    or  .

    It gives 6 different solutions for  in the interval [0,):

    ,  ,  ,  ,  ,   .



2)   =   ====>   =   or    or    or    or    or  .

    It gives 6 different solutions for  in the interval [0,):

    ,  ,  ,  ,  ,   .


The final answer is the union of values of  from the lists 1) and 2).


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