David's Mathematics Talk

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~?

csc =cosecant

sec =secant

cot=cotangent

David:

i know a~

David:

so......我點help u ar~

it's easy la~

David:

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

David:

7> tan square @ +1 = sec square @

8> cot square@ +1 = csc square @

OK ma?

David:

ok~照代番入去之ma~

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

THX

David:

yes a

so i fell down in class

David:

7都唔難

coz u dun familiar w/ 8 ma

David:

hahah~原來全部都唔難

^^

David:

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

u wanna know how i'm stupid ma?~

David:

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

David:

nonono~

y

tutor said

there's 2 method 2do

David:

sec@ = 1/cos@

so........

sec square@ = 1/cos square@

stupid fish nae~

David:

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

David:

haha gum魚魚dou多餘~~

David:

7~8只不過係之前o個d make出黎ga咋!

@_@

David:

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

David:

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!

ok ma~?

wait

David:

sin sq@ + cos sq@ = 1

so.........

sin sq@ = 1 - cos sq@

cos sq@ = 1 - sin sq@

where'S the "-1"?

David:

then...先通到分+ma~

ok ma~?

yup~

David:

Q2> This first

David:

ok

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

@o@" ~~

David:

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

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

-_-"

David:

haha~呢個可唔可以聽日先ans u ar~?

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

(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 !

(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@