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Thread: another problem ><

  1. #1
    Newbie Phoenixium's Avatar
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    another problem ><

    im good at nearly all maths topics but god i fail at trigonometry so much lol anywho...

    find all possible solutions for θ within the range 0 < θ < 2Pi that satisfy

    tanθ = tanα

    where α > 0

    i dont even know how to go about starting this let alone answering it ^^
    so can anyone talk me through this? muchly appreciated and mega-thanks in advance
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Phoenixium View Post
    im good at nearly all maths topics but god i fail at trigonometry so much lol anywho...

    find all possible solutions for θ within the range 0 < θ < 2Pi that satisfy

    tanθ = tanα

    where α > 0

    i dont even know how to go about starting this let alone answering it ^^
    so can anyone talk me through this? muchly appreciated and mega-thanks in advance
    Since $\displaystyle \alpha$ is just a constant, you can think of this as trying to find where the graph of $\displaystyle tan(/theta)$ intersects the line $\displaystyle y = tan(\alpha)$. Glancing at the graph below, which has a sample line running through it, you can see that the function $\displaystyle y = tan(\theta)$ has a period of $\displaystyle \pi$. Thus you will have two possible solutions in the given range.

    So the possible values of $\displaystyle \theta$ are
    $\displaystyle \theta = \alpha + n \pi$ where n = 0, 1

    -Dan
    Attached Thumbnails Attached Thumbnails another problem &gt;&lt;-tangent.jpg  
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  3. #3
    Newbie Phoenixium's Avatar
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    Feb 2008
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    thanks that helped so much ^^
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