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Forum: General Questions - High School/Secondary
Welcome to the General Questions - High School/Secondary forum!
For discussing questions from any discipline at high school/secondary school level.

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jump to page: << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 >> of 53 (262 items)

Straightedge Only Construction by Bractals on 2009-08-27 04:55:48
Need help with a geometry problem.

Given a circle, a diameter AB of the circle, and two lines tangent to the circle at points A and B.

Is it possible to construct the center of the circle with a straightedge only?
[ reply | up ]
Help on trigonometric identity by cnx on 2009-08-16 08:08:19
Hello everybody,

I need some help to prove the following trigoometric identity:

For all positive odd integers n=2m+1,
\sin^2(\frac{\pi}{n}) \cdot \sin^2(\frac{2\pi}{n})...\sin^2(\frac{m\pi}{n})=\prod_{k=1}^{m} \sin^2(\frac{k\pi}{n})= \frac{n}{2^{n-1}}

I checked this for n=3,5,7 and need to use it for the proof of another identity. Could someone help me on this one, please? Thanks.
[ reply | up ]
Parity of the tau function by dh2718 on 2009-05-16 06:12:35
 Pahio's entry about the parity of the tau function gives the answer to an old riddle which I reproduce here:

 There are 100 lamps numbered from 1 to 100. Each one has its own push-button switch, which toggles its lamp from ON to OFF or from OFF to ON. At the beginning, all the lamps are off. 100 persons walk along the switches an pushes some of them. The first one pushes all the switches, the second one pushes all the even switches, the third one pushes switches 3, 6, 9... the last one pushes only switch 100.
 The question is which lamp remains ON at the end?
[ reply | up ]
Symmetric function by curious on 2009-05-13 17:42:56
If f(x) is symmetric around x = c, does g[f(x)] have to be symmetric around that point?
I illustrate my question with this example:

If \integral (from x=0 to x= \pi/2) sin x dx = (1/2)*\integral (from x=0 to x=\pi) sin x dx,

then is this necessarily true:

\integral (from x=0 to x=\pi/2) e^(sin x) dx = (1/2)*\integral (from x=0 to x=\pie) e^(sin x) dx ??

If yes, can you prove it?

Thanks
[ reply | up ]
Jordan's Lemma by curious on 2009-05-11 13:23:48
Please take a look at the following proof of Jordan's Lemma:
http://mathworld.wolfram.com/JordansLemma.html

How did he move from eq (7) to (8) to (9) and then to (10)? Can you please explain?

How did he go from (8) to (9), i.e. change the limits of integration in (9)?

Does anyone know an alternative, clearer and easier to understand, proof?

Thanks.
[ reply | up ]

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