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Math Help - another trig limit problem (but this time I think I know what im doing)

  1. #1
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    another trig limit problem (but this time I think I know what im doing)

    another trig limit problem (but this time I think I know what im doing)-screen-shot-2012-10-24-1.33.23-am.png

    can I divided the numerator and denominator by theta and thus get the form 0/1=0 ?
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  2. #2
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    Re: another trig limit problem (but this time I think I know what im doing)

    Hello, kingsolomonsgrave!

    \displaystyle\lim_{\theta\to0}\frac{\cos\theta-1}{\sin\theta}

    Can I divide the numerator and denominator by theta and thus get the form 0/1=0 ?

    Yes, you can! . . . Good thinking!


    Another approach:

    \frac{\cos\theta - 1}{\sin\theta} \;=\;\frac{-(1-\cos\theta)}{\sin\theta} \;=\;-\frac{1-\cos\theta}{\sin\theta}\cdot\frac{1+\cos\theta}{1+  \cos\theta} \;=\;-\frac{1-\cos^2\theta}{\sin\theta(1+\cos\theta)}

    . . . . . . . =\;-\frac{\sin^2\theta}{\sin\theta(1+\cos\theta)} \;=\; \frac{-\sin\theta}{1+\cos\theta}


    Therefore: . \displaystyle \lim_{\theta\to0}\frac{-\sin\theta}{1+\cos\theta} \;=\;\frac{0}{2} \;=\;0

    Thanks from kingsolomonsgrave
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