Sajang Yang: Writing LaTeX Math Formula on blogger.com: How to get the max rectangle inscribed in the unit circle

Thursday, November 11, 2010

I have read a QnA: http://www.google.com/support/forum/p/blogger/thread?tid=7e58a91b313290a9&hl=en

Maybe it's worthy to try the way how to write a LaTeX math formula in the post.

How to find the dimension of the maximum of the area of a rectangle inscribed in the unit circle:

$x=2\cdot cos\theta$
$y=2\cdot sin\theta$
$A=xy=2cos\theta \cdot 2sin\theta =2\cdot(2cos\theta sin\theta) =2sin2\theta$
$\frac{dA}{d\theta}=2\cdot cos2\theta \cdot 2 = 4\cdot cos2\theta$
$4cos2\theta = 0 = cos2\theta$
$2\theta = cos^{-1}0$
$2\theta = \frac{\pi}{2}$
$\theta = \frac{\pi}{4}$
$x=2cos\theta=2 \cdot \frac{1}{\sqrt{2}}=\sqrt{2}$
$y=2sin\theta=2 \cdot \frac{1}{\sqrt{2}}=\sqrt{2}$
$\therefore the\ dimension\ is\ \sqrt{2}\times \sqrt{2}$

Hmm... not bad for the first trial, is it?

Sajang Yang

Thursday, November 11, 2010

Writing LaTeX Math Formula on blogger.com: How to get the max rectangle inscribed in the unit circle

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