sin 10 . sin 30 . sin 50 . sin 70 equals to?

Question

You're genius if you can solve this,
I'll give 10 points for the first right answer.

Answer 1

the correct answer is 0.0625

Answer 2

2

Answer 3

1/16
and i didnt use a calculator

heres how i got it
im assuming you know the basics of trigonometry otherwise this problem is too advanced i think you know that
cosa-cosb=2sin((a+b)/2)cos((a-b)/2)
sina-sinb=2cos((a+b)/2)sin((a-b)/2)
i dont know why those ... appear but point at them to see it
so here it goes
sin 10 . sin 30 . sin 50 . sin 70
=1/2(sin 10 . sin 50 )( sin 70)
=1/4(cos40-cos60)(sin70)
=1/4(cos40sin70-1/2sin70)
=1/4(1/2(sin110-sin30)-1/2sin70)
=1/4(1/4)
=1/16

im hoping that this can be my first best answer

Answer 4

Sin 10.1/2.sin50.sin70
1/2(sin10.sin50.sin 70)
1/2(sin10(1/2(cos20-cos120)))
1/2(sin10(1/2(cos20+1/2)))
1/2(sin10(1/2cos20+1/4))
1/2(1/2sin10cos20+1/4sin10)
1/4sin10cos20+1/8sin10
1/4(1/2(sin30-sin10)+1/8sin10
1/8(1/2-sin10)+1/8sin10
1/16-1/8sin10+1/8sin10
1/16

Answer 5

sin 10= 0.173648177
sin 30= 0.5
sin 50= 0.766044443
sin 70= 0.93969262

0.173648177 x 0.5 x 0.766044443 x 0.93969262
= 0.062499999

im not sure f my answer is correct....hehe...

Answer 6

sin 10=0.173648
sin30=0.5
sin50=0.766044431
sin70=0.93969208

Answer 7

sin 10=0.173648
sin30=0.5
sin50=0.766044431
sin70=0.93969208

Answer 8

thats pretty impressive! how did you guys know that it's 1/16 without using a calculator?
how did you guys know the values of sin 10, sin 50 and sin 70? please elaborate. thanks.

Answer 9

THE ANSWER IS 0.0625 = 1/16

Answer 10

0.0625 or 1/16