David's Mathematics Talk

David's Mathematics Talk

魚:

math@_@~~fish feel dizzy...

tell u 8 rules 1st

1> csc@ = 1/ sin@

2> sec@ = 1/ cos@

3> cot@ = 1/ tan@

4> tan@ = sin@ /cos@

5> cot@ = cos@ /sin@

David:

csc~? sec? cot? <---咩黎ga~?

魚:

csc =cosecant

sec =secant

cot=cotangent

David:

未學bor~

魚:

i know a~

read rule 1-3~~

David:

so......我點help u ar~

魚:

it's easy la~

David:

妳繼續la咁

魚:

6> sin square @ + cos square @ =1 (u know this la~)

David:

頭5條都無咩問題bor~

魚:

7> tan square @ +1 = sec square @

8> cot square@ +1 = csc square @

OK ma?

David:

ok~照代番入去之ma~

魚:

but fish@_@ nae

here comes two hard question:

sec square@+csc square@ = sec square@ x csc square @

prove they are equal

David:

wait~眕清楚d式先

魚:

THX

David:

係7,8 o個2條麻煩o者

魚:

yes a

so i fell down in class

David:

7都唔難

魚:

coz u dun familiar w/ 8 ma

David:

hahah~原來全部都唔難

魚:

David:

計下妳條數先ar下

妳o個條數都唔難丫~

妳有冇計過ga先?

魚:

i got a huge mess!......@_@

u wanna know how i'm stupid ma?~

David:

妳頭先列晒咁多式la~

妳照住將佢代入去睇下

魚:

step1> 1+tan sq@+1+cot sq@=(1+tan sq@)(1+cot sq@)

David:

nonono~

魚:

tutor said

there's 2 method 2do

David:

sec@ = 1/cos@

so........

sec square@ = 1/cos square@

魚:

stupid fish nae~

David:

基本上黎講, 7~8呢2條係可以唔理佢ga!

魚:

......so i @_@ lol

David:

多餘的!

魚:

haha gum魚魚dou多餘~~

David:

7~8只不過係之前o個d make出黎ga咋!

記左,可能會方便d o既 , but........唔記都無咩問題 (but要知佢點黎先)

魚:

@_@

David:

妳知唔知7~8呢2條野點黎ga~?

魚:

7> sin sq@ / cos sq@ + sin sq@+cos sq@ = 1/cos@.........???

David:

睇住喇

tan sq@ = sec sq@ - 1

tan sq@ = 1/cos sq@ - 1 <---其實最緊要都係要識通分

only睇右邊!

通分la~ 1-cos sq@ / cos sq@

因為1-cos sq@ = sin sq@ , so......................就會= sin sq@ / cos sq@, 即係 tan sq@

ok ma~?

魚:

wait

David:

sin sq@ + cos sq@ = 1

so.........

sin sq@ = 1 - cos sq@

cos sq@ = 1 - sin sq@

魚:

通分la~ 1-cos sq@ / cos sq@

where'S the "-1"?

David:

通左分law~

妳當 1 = cos sq@ / cos sq@

then...先通到分+ma~

ok ma~?

最緊要係識通分! then..呢2條式點黎,妳就好清楚ga喇

快手d喇! 我要訓喇,唔係俾人嘈呢! (becox...my dad 就起身喇)

魚:

yup~

David:

識了?

魚:

Q2> This first

David:

魚:

(sin@-cos@)/(tan@-cot@)=(sin@cos@)/(sin@+cos@)

@o@" ~~

Q1 i answer u tmr(try)

David:

有d眕頭wor呢條! 妳睇清楚有冇打錯題目ar下

魚:

LHS= ( sin@ - cos@ ) / ( tan@ - cot@)

RHS= ( sin@ cos@ ) / (sin@ + cos@ )

-_-"

David:

haha~呢個可唔可以聽日先ans u ar~?

唔得喇,我要訓喇! 俾人嘈喇>.<

聽日ans u la~

i e-mail to u la~! (maybe)

<June 8, 2004>

solution @ June 9, 2004

L.H.S. = sin@ - cos@ / tan@ - cot@ = sin@ - cos@ / ( sin@/cos@ - cos@/sin@ ) 備注: tan@ = sin@/cos@ and cot@ = cos@/sin@ = sin@ - cos@ / ( sin sq@ - cos sq@ / sin@cos@ ) 備註 : 通分ar! 成日要用ga! 記住ar! = sin@ - cos@ / [(sin@+cos@)(sin@-cos@) / sin@cos@] 備注 : a sq - b sq = (a+b)(a-b) 唔係唔記得左下fa? = sin@cos@ / sin@ + cos@ <---約簡! 呢步可能難d , but我諗妳睇到ga喇 ! = R.H.S 記住 ~ (1) csc@ = 1 / sin@ (2) sec@ = 1 / cos@ (3) cot@ = 1 / tan@ (4) tan@ = sin@ / cos@ , so........cot@ = cos@ / sin@ (5) sin sq@ + cos sq@ = 1 , so......... sin sq@ = 1 - cos sq@ and cos sq@ = 1 - sin sq@ <---要記得呢d ga ! 以上要必記的! 呢d就......................記唔記都得,要知點黎就得喇! (6) tan sq@ + 1 = sec sq@ tan sq@ = sec sq@ - 1 tan sq@ = 1 / cos sq@ - 1 tan sq@ = 1 - cos sq@ / cos sq@ (通分ai , 將 1 轉做 cos sq@ / cos sq@) tan sq@ = son sq@ / cos sq@ tan sq@ = tan sq@ (7) cot sq@ + 1 = csc sq@ cot sq@ = csc sq@ - 1 cos sq@ / sin sq@ = 1 / sin sq@ - 1 cos sq@ / sin sq@ = 1 - sin sq@ / sin sq@ (又通分喇bor~!) cos sq@ / sin sq@ = cos sq@ / sin sq@ 搞掂~^^~ 有d野睇唔清楚 , 搵張paper寫出黎 , 咁會易d計 + 易d記 !