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Math Help - Tangent...Help please

  1. #1
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    Tangent...Help please

    Hello!


    I have to solve this

    tan 3θ = 0

    what is then θ

    there should be three values...

    but my range is between -pi to +pi
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  2. #2
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    What have you tried?
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  3. #3
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    my teacher said i came to that point...so it is OK...but from noe on i am stuck
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  4. #4
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    Hello, domenfrandolic!

    There are five solutions.


    \text{Solve: }\;\tan 3\theta \:=\: 0\quad\text{ for }\text{-}\pi < \theta < +\pi

    We have: . \tan3\theta \:=\:0

    Then: . 3\theta \:=\:\hdots\;\text{-}4\pi,\;\text{-}3\pi,\;\text{-}2\pi,\;\text{-}\pi,\;0,\;\pi,\;2\pi,\;3\pi,\;4\pi\;\hdots

    Hence: . \theta \;=\;\hdots\;\text{-}\tfrac{4\pi}{3},\;\text{-}\pi,\;\text{-}\tfrac{2\pi}{3},\;\text{-}\tfrac{\pi}{3},\;0,\;\tfrac{\pi}{3},\;\tfrac{2\pi  }{3},\;\pi,\;\tfrac{4\pi}{3}\;\hdots

    Therefore: . \theta \;=\;\left\{\text{-}\frac{2\pi}{3},\;\text{-}\frac{\pi}{3},\;0,\;\frac{\pi}{3},\;\frac{2\pi}{3  }\right\}

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