^o^"懂"就是聰明Maths

since sin x = 3/5 , cos x = 4/5 for x is acute
cos2(x/2) = 4/5
1 - 2sin^2 (x/2) = 4/5
sin^2 (x/2) = 1/10
sin (x/2) = (√10) / 10

sin^2(x/2)+cos^2(x/2) = 1
cos^2 (x/2) = 9/10
COS (x/2) = (3√10)/10

tan (x/2) = (√10) / 3 (√10) = 1/3

2010-09-17 18:43:16 補充：
sin x = 3/5
sin^2 x = 9/25
1-cos^2 x = 9/25
cos^2 x = 16/25
cos x = 4/5 or cos x = -4/5( reject, since x is acute )
cos x = 4/5

all of these 2 are good, i can't make any decision....

sin x=3/5

圖片參考：http://imgcld.yimg.com/8/n/HA00704496/o/701009170077013873371710.jpg

Let x/2=a
cos(a+a)
=(cos a)^2-(sin a)^2
=(cos a)^2-[1-(cos a)^2]
=(cos a)^2-1+(cos a)^2
=2(cos a)^2-1
Since 2a=x
cos x=2(cos x/2)^2-1
(cos x)+1=2(cos x/2)^2
(1/2)[(cos x)+1]=(cos x/2)^2

(cos x/2)^2
=(1/2)[(cos x)+1]
=1/2(1+4/5)=(1/2)(9/5)=9/10
cos x/2=3/root(10)

圖片參考：http://imgcld.yimg.com/8/n/HA00704496/o/701009170077013873371721.jpg

sin x/2=1/root(10)
tan x/2=1/3
Answer: cos x/2=3/root(10),sin x/2=1/root(10),tan x/2=1/3

2010-09-17 22:00:12 補充：
圖畫醜了些，不要見怪。