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Thread: Rearranging an equation using a simple trigonometric identity

  1. #1
    Newbie evanator's Avatar
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    Rearranging an equation using a simple trigonometric identity

    Hi all,

    I have a mental block on a certain very simple trigonometry problem. I know I will slap my forehead when I see the solution. I therefore ask for your indulgence and thank, in advance, any responders. Here is the question and my attempt:

    Using $\displaystyle \tan \theta \equiv \frac{\sin \theta}{\cos \theta}$, show that the equation $\displaystyle \tan \theta = \sin \theta$ can be written as $\displaystyle \sin \theta (\cos \theta - 1) = 0$ provided that $\displaystyle \cos \theta \neq 0$.

    Here is what I have done already:

    $\displaystyle \tan \theta = \sin \theta$

    $\displaystyle \sin \theta = \frac{\sin \theta}{\cos \theta}$

    $\displaystyle \sin \theta = \sin \theta \cos \theta$

    $\displaystyle \cos \theta = 1$

    I am not at all sure that I am on the right track. Any help would be sincerely appreciated.

    Regards,

    Evanator
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by evanator View Post
    Hi all,

    I have a mental block on a certain very simple trigonometry problem. I know I will slap my forehead when I see the solution. I therefore ask for your indulgence and thank, in advance, any responders. Here is the question and my attempt:

    Using $\displaystyle \tan \theta \equiv \frac{\sin \theta}{\cos \theta}$, show that the equation $\displaystyle \tan \theta = \sin \theta$ can be written as $\displaystyle \sin \theta (\cos \theta - 1) = 0$ provided that $\displaystyle \cos \theta \neq 0$.

    Here is what I have done already:

    $\displaystyle \tan \theta = \sin \theta$

    $\displaystyle \sin \theta = \frac{\sin \theta}{\cos \theta}$

    $\displaystyle \sin \theta = \sin \theta \cos \theta$

    starting from the above step ...

    $\displaystyle 0 = \sin{t}\cos{t} - \sin{t}$

    $\displaystyle 0 = \sin{t}(\cos{t} - 1)$
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  3. #3
    Newbie evanator's Avatar
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    I was right. It was a doh! moment. Thank you very much, skeeter.
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