A MATHS 一問

cyris

大家都仲係唔明....

你會唔會走去見到4COS^3 X-3COS X就會用COS3X開始推-V-

如果係背既話我冇野講了....當佢OUT C吧
韓信 發表於 3-5-2009 09:27

加油啊韓信,我知你a到

韓信

我諗我A唔到-_-

做PAST PAPER都覺得好淺

一做呢D騎呢野就摸不著頭腦

Hitler

99年paper2
第8題(a)part

Zend

treated it as double angle formula
(who told you amaths does not require memorization? huh?)

and in Pmaths, you can form equation by using De Moivre's theorem ....

cla981085

大家都仲係唔明....

你會唔會走去見到4COS^3 X-3COS X就會用COS3X開始推-V-

如果係背既話我冇野講了....當佢OUT C吧
韓信 發表於 3-5-2009 09:27

我會-v-..
有時L.H.S.唔得,,咪用R.H.S. lo..
有時我兩邊一齊唻..
如果要對付一d好複雜既數,,兩邊一齊計就好快ko..好好使的.

又或者如果你想靚仔d既,,想寫到由L.H.S.變到R.H.S.,你可以係草稿寫左個proof (from R.H.S. to L.H.S.)
之後般返去answer book時就調返轉..
例如:

以上係由我之前個proof調返轉的

[H]唔女問我

- -呢個做學校試卷做過( PROVE COS3X定唔記得SIN3X)...跟住有個同學一野寫答案....
好似一分都冇...原來係佢阿哥叫佢背[[bao_35]] sosad

Zend

4COS^3 X-3COS X

COS2X=2COS^2X -1
4CO3^3X-3COSX = 2COSX(2COS^2X-1) -COSX
=2COSXCOS2X-COSX
=2 [1/2 (cos3x +cos(-x)) ] -cosx
=cos3x+cosx-cosx
=cos3x
from destruction to construction

By De Movire's theorem
(cosx+isinx)^3 = cosx^3 +3cos^2xsinx i +3cosxsin^2x (i)^2 +sin^3 x i ^3= cos3x+isin3x

We have
cos3x = cos^3x -3cosxsin^2x  (i^2 = -1)
=cos^3x -3cosx(1-cos^2x) = cos^3x -3cosx+3cos^3x = 4cos^3x - 3cosx
sin3x = 3cos^2xsinx -sin^3x = 3(1-sin^2x)sinx-sin^3x = 3sinx-3sin^3x-sin^3x = 3sinx-4sin^3x
i^3 = -i

以前的DM THEOREM 係IN C 的,所以唔使叫你地PROVE NE 樣野
但現在係OUT-C 所以得閒出一題都唔出奇

-終場ソ使者-

我會-v-..
有時L.H.S.唔得,,咪用R.H.S. lo..
有時我兩邊一齊唻..
如果要對付一d好複雜既數,,兩邊一齊計就好快ko..好好使的.

又或者如果你想靚仔d既,,想寫到由L.H.S.變到R.H.S.,你可以係草稿寫左個proof (from R.H ...
cla981085 發表於 3-5-2009 14:27

我想問你第一步點解要拆出黎先
如果你冇用cos3x去計4cos³x-3cosx你會唔會識咁拆?
你可能會寫左cos³x+3cos³x-cosx-2cosx

小莓。改

Zend 又用pure野屈人?
用埋那些可惡的:
(cosx + isinx)^n = R(x) + I(x)
又要這個 : e^(pi*i) = -1

韓信

上面開始有D已眉目

有D用PURE MATHS 有D直頭PROVE到

其實我諗MARKING果條友都係背出黎= ="所以諗黎哂氣

會考應該唔會出到咁