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Math Help - Find the smallest number

  1. #1
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    Find the smallest number

    Find the smallest number-findthesmall.jpg Click image to enlarge.
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    MHF Contributor MarkFL's Avatar
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    Re: Find the smallest number

    Hint: \sin(\theta)=\sin(\theta+2k\pi) where k\in\mathbb{Z}.
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    Re: Find the smallest number

    Nope. Textbook says this Find the smallest number-text.jpg
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    MHF Contributor MarkFL's Avatar
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    Re: Find the smallest number

    Use the hint I gave in conjunction with the hint your book provides (which I assumed you already knew).

    \sin\left(\frac{\pi}{4} \right)=\frac{1}{\sqrt{2}}

    \sin(\theta)=\sin(\theta +14\pi)
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    Re: Find the smallest number

    Well, I'm not sure if this way works but it gave me the right answer. If \sin(\theta)= Sqrt 2/2 then that means the radian must be at pi/4. So I came up with a formula that looks like this. (4n+1)pi over 4. So I just plugged in 14 into n and I got my answer.
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    MHF Contributor MarkFL's Avatar
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    Re: Find the smallest number

    Yes:

    \frac{1}{\sqrt{2}}=\sin\left(\frac{\pi}{4} \right)=\sin\left(\frac{\pi}{4}+14\pi \right)=\sin\left(\frac{(4\cdot14+1)\pi}{4} \right)=\sin\left(\frac{57\pi}{4} \right)
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    Re: Find the smallest number

    There is NO such "smallest number" but there is an obvious smallest positive number.
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