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Math Help - understanding a step in proving that limit as x->0 of sinx/x =1

  1. #1
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    understanding a step in proving that limit as x->0 of sinx/x =1

    as part of the proof that sinx/x=1 or x/sinx=1 we have this picture ->understanding a step in proving that limit as x->0 of sinx/x =1-picture-13.png


    I don't understand how they got from part 1 to part 2 of that.
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    Re: understanding a step in proving that limit as x->0 of sinx/x =1

    Quote Originally Posted by kingsolomonsgrave View Post
    as part of the proof that sinx/x=1 or x/sinx=1 we have this picture ->Click image for larger version. 

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    I don't understand how they got from part 1 to part 2 of that.
    Assuming that you are working with \displaystyle \begin{align*} \theta > 0, \cos{\theta} > 0 \end{align*}, then we have

    \displaystyle \begin{align*} \theta &< \frac{\sin{\theta}}{\cos{\theta}} \\ \theta \cos{\theta} &< \sin{\theta} \\ \cos{\theta} &< \frac{\sin{\theta}}{\theta} \end{align*}
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    Re: understanding a step in proving that limit as x->0 of sinx/x =1

    thanks! I get it now
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