m2 trigo

a)y= sin20° sin40° sin60° sin80°= √3/2 sin80° sin40° sin20°= √3/2 cos10°cos50°cos70°
b)y sin10°= √3/2 cos10°cos50°cos70° sin10°
= √3/4 sin20° cos50°cos70°
= √3/8 sin20° (cos120° + cos20°)
= -√3/16 sin20° + √3/8 sin20°cos20°
= √3/16 (sin40° - sin20°)
= √3/16 (2 cos30° sin10°)
= √3/16 (√3 cos80°)
= 3/16 cos80°


2012-05-07 23:47:20 補充：
Method 2 :

y = sin20° sin40° sin60° sin80°

= √3/2 sin20° sin40° sin80°

= (√3/2) (-1/2)(cos60° - cos20°)sin80°

= (√3/2) [(-1/4)sin80° + (1/2)sin80°cos20°]

= (√3/2) [(-1/4)sin80° + (1/4)(sin100° + sin60°)]

= (√3/2) [(-1/4)sin80° + (1/4)(sin80° + sin60°)]

2012-05-07 23:47:42 補充：
= (√3/2) (1/4)sin60°

= (√3/2) (1/4)(√3/2)

= 3/16

So y sin10° = 3/16 cos80°

Can you show me your method ?

2012-05-08 13:07:28 補充：
Your teacher used 13 steps to do (b) , may be his or her steps are detail , so we cann't
say a method is good or bad according to the number of the steps.

2012-05-08 13:07:41 補充：
For example , the method above can be simplify to 5 steps

y sin10° = √3/2 cos10°cos50°cos70° sin10°
= √3/4 sin20° cos50°cos70°
= √3/8 sin20° (cos20° + cos120°)
= √3/16 (sin40° - sin20°)
= √3/16 (2 cos30° sin10°)
= 3/16 cos80°

2012-05-08 13:07:47 補充：
Also method 2 can be simplify to 4 steps :

y sin10° = sin20° sin40° sin60° sin80° sin10°
= (√3/2) (-1/2)(cos60° - cos20°)sin80° sin10°
= (√3/2) [(-1/4)sin80° + (1/4)(sin100° + sin60°)] sin10°
= (√3/2) (1/4) sin60° sin10°
= 3/16 cos80°

39 : 2 !!??

=_=

好 彩 你 選 擇 投 票.

y = √3/2 cos 10 cos 50 cos 70 . . . . . . . . . . . (from part a)
==> y = √3/4 cos 50 (cos 80 + cos 60) . . . . . . (cos 60 = 1/2)
==> y = √3/4 cos 50 cos 80 + √3/8 cos 50
==> y = √3/8 (cos 130 + cos 30) + √3/8 cos 50
==> y = -√3/8 cos 50 + 3/16 + √3/8 cos 50 . . . (cos 30 = √3/2)
==> y sin 10 = 3/16 cos 80 . . . . . . . . . . . . . . .(sin 10 = cos 80)