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- Nov 1st 2012, 03:45 PMEraser147Find the smallest number
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- Nov 1st 2012, 03:47 PMMarkFLRe: Find the smallest number
Hint: $\displaystyle \sin(\theta)=\sin(\theta+2k\pi)$ where $\displaystyle k\in\mathbb{Z}$.

- Nov 1st 2012, 03:50 PMEraser147Re: Find the smallest number
Nope. Textbook says this Attachment 25514

- Nov 1st 2012, 04:00 PMMarkFLRe: Find the smallest number
Use the hint I gave in conjunction with the hint your book provides (which I assumed you already knew).

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

$\displaystyle \sin(\theta)=\sin(\theta +14\pi)$ - Nov 1st 2012, 04:01 PMEraser147Re: Find the smallest number
Well, I'm not sure if this way works but it gave me the right answer. If $\displaystyle \sin(\theta)$= 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.

- Nov 1st 2012, 05:43 PMMarkFLRe: Find the smallest number
Yes:

$\displaystyle \frac{1}{\sqrt{2}}=\sin\left(\frac{\pi}{4} \right)=\sin\left(\frac{\pi}{4}+14\pi \right)=\sin\left(\frac{(4\cdot14+1)\pi}{4} \right)=\sin\left(\frac{57\pi}{4} \right)$ - Nov 1st 2012, 07:10 PMHallsofIvyRe: Find the smallest number
There is NO such "smallest number" but there is an obvious smallest

**positive**number.