F.2 Maths x1(?)

吾一定岩,當參考

a(i)
cos∠ABC=4/8
∠ABC=60度

a(ii)
∠DBC =∠DBA=60度/2
∠DBC =30度

a(iii)
cos∠DBC=4/BD
cos 30度=4/BD
BD=4.618802154
sin∠BDC=4/BD
∠BDC=60度

b
△BCD is similar to△ABC
sin∠CDB=4/BD
sin60=4/BD
BD=4/sin60度
BD=4.619(Corr. to 4 isg. fig.)

c依題吾係好肯定,參考下算啦
Using the result of part (a) and (b)
cos 2Θ = 2cosΘ
L.H.S
cos 2Θ
=cos2(60度)
=cos 120度
=-0.5
R.H.S
2cosΘ
=2 cos 60度
=2x4/8 依度用番ai 個ans
=1
thereforcos 2Θ =/ 2cosΘ
so cos 2Θ = 2cosΘ isn't always true

一張三角形既圖:
http://img205.imageshack.us/img205/6246/41679804.png

In the figure, ABC is a right-angled triangle, AB = 8, BC =4 and ∠ABC= ∠DBC.
(a) Find the measures of the following angles.
(i) ∠ABC ====> 60 degree ( cos∠ABC = 1/2 )
(ii) ∠DBC ====> 60 degree ( because = ∠ABC; 但唔合理的 )
(iii) ∠BDC ====> 30 degree 但因為題目有問題, 這個問題也是不恰當的.

(b)write down a triangle similar to △ABC. Hence, find the length of BD, correct to 4 sig.fig.

BD/BC = cos∠BDC
==> BD / BC = (Square-root(3)) / 2
==> BD = 4 x 1.7321 = 6.9282

(c) Using the results of parts (a) and (b), determine whether cos 2Θ = 2cosΘ is always true.


2010-08-07 23:54:20 補充：
(ii) ∠DBC ====> 60 degree ( because = ∠ABC; 但唔合理的 )
According to the figure, the answer should be 30 degree.
(iii) ∠BDC ====> 30 degree 但因為題目有問題, 這個問題也是不恰當的.
According to the figure, the answer should be 60 degree.

2010-08-07 23:54:35 補充：
(c) Using the results of parts (a) and (b), determine whether cos 2Θ = 2cosΘ is always true

CAN'T do that

條問題有問題∠ABC= ∠DBC是不可能.