F3 Trigonometry

As follows:

圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/03-67.jpg


2010-05-30 14:59:20 補充：
http://i707.photobucket.com/albums/ww74/stevieg90/03-67.jpg

In the figure, AEB and BDC are straight lines.
(a)(i) Find the length of AD and express your answer in terms of θ.
1/AD=cosθ
1=ADcosθ
1/cosθ=AD

(ii) Find the length of AE and express your answer in terms of θ and α.
AD=1/cosθ
AE/AD=cosα
AE/(1/cosθ)=cosα
AEcosθ=cosα
AE=cosα/cosθ

(b)(i) Find the length of CD and express your answer in terms of θ.
CD/1=tanθ
CD=tanθ

(ii) Find the length of BE and express your answer in terms of θ and surd form.
CD=tanθ
BD=1-CD
BD=1-tanθ
BE/BD=cos45
BE/(1-tanθ)=cos45............cos45=(√2)/2
BE=(1-tanθ)(√2)/2
BE=√2(1-tanθ)/2

2010-05-30 15:17:42 補充：
AE=cosα/cosθ
AE=1
BE=AB-AE
BE=√2-1
BE=√2(1-tanθ)/2
√2-1=√2(1-tanθ)/2
2(√2-1)=√2(1-tanθ)
2(√2-1)/√2=1-tanθ
[ 2(√2-1)/√2 ] (√2/√2)=1-tanθ
2√2(√2-1)/2=1-tanθ
√2(√2-1)=1-tanθ
2-√2=1-tanθ
1-2-√2=tanθ
√2-1=tanθ