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標題: [Core] F4 Math - Trigonometry (1) [打印本頁]

作者: Steven2011 時間: 2011-7-24 04:18 PM 標題: F4 Math - Trigonometry (1)

1a)求證sin(x-270度)= cos x 是恆等
睇象限?

1b)由此化簡,,,sinx cos(90度-x) – (  sin( x-270度)cos(180-x)  )

2)試用sin x 表示 (  1    / (1+cosx) )    + (  1    /    (1-cos x)  )

3)己知tan x+ tan(90-x) =3  ,,求tan^2  x +  ( 1 /    tan^2  x )
點解唔係就甘2次==

4)己知sinx +coxx = k ,,用k表示 sinxcosx

5)COSX ( 3sinx+2) = 0
唔係甘做咩    COSX = 1    / (SINX+2)
                           SINX / COS X =  1/2咩

作者: 夏娜醬大好 時間: 2011-7-24 04:41 PM

1.
(a) 你可以靠睇
亦可以做：
sin(x-270) = sin(x+90) = sin(180-x-90) = sin(90-x) = cosx
(b) sin(x)cos(90-x) - sin(x-270)cos(180-x)
= (sinx)^2 + (cosx)^2
= 1

2.
1/(1+cosx) + 1/(1-cosx)
= (1-cosx+1+cosx)/[1-(cosx)^2]
= 2/(sinx)^2

3.
tanx+tan(90-x) = 3
tanx+1/tanx = 3

(tanx)^2+1/(tanx)^2
= (tanx)^2+1/(tanx)^2 +2-2
= (tanx+1/tanx)^2 -2
= 3^2 -2
= 7

4.
sinx+cosx = k
(sinx)^2+(cosx)^2+2sinxcosx = k^2
1+2sinxcosx = k^2
sinxcosx = (1/2)(k^2-1)

5.
cosx(3sinx+2) = 0
cosx = 0 or 3sinx+2 = 0
cosx = 0 or sinx = -2/3

作者: Steven2011 時間: 2011-8-7 02:14 PM

THX YOU SO MUCH

= (tanx)^2+1/(tanx)^2 +2-2
= (tanx+1/tanx)^2 -2 <<<<<<WHY仲有2 GE 唔係2-2 =0 唔明= =

作者: 夏娜醬大好 時間: 2011-8-7 02:27 PM

Note that (tanx)^2+1/(tanx)^2 +2 = (tanx+1/tanx)^2

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