# Find the smallest number

• Nov 1st 2012, 04:45 PM
Eraser147
Find the smallest number
Attachment 25512 Click image to enlarge.
• Nov 1st 2012, 04:47 PM
MarkFL
Re: Find the smallest number
Hint: $\sin(\theta)=\sin(\theta+2k\pi)$ where $k\in\mathbb{Z}$.
• Nov 1st 2012, 04:50 PM
Eraser147
Re: Find the smallest number
Nope. Textbook says this Attachment 25514
• Nov 1st 2012, 05:00 PM
MarkFL
Re: Find the smallest number
Use the hint I gave in conjunction with the hint your book provides (which I assumed you already knew).

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

$\sin(\theta)=\sin(\theta +14\pi)$
• Nov 1st 2012, 05:01 PM
Eraser147
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.
• Nov 1st 2012, 06:43 PM
MarkFL
Re: Find the smallest number
Yes:

$\frac{1}{\sqrt{2}}=\sin\left(\frac{\pi}{4} \right)=\sin\left(\frac{\pi}{4}+14\pi \right)=\sin\left(\frac{(4\cdot14+1)\pi}{4} \right)=\sin\left(\frac{57\pi}{4} \right)$
• Nov 1st 2012, 08:10 PM
HallsofIvy
Re: Find the smallest number
There is NO such "smallest number" but there is an obvious smallest positive number.