Question

sin20.sin40.sin80=?

Answer 1

Are the numbers in degrees or rads?

Answer 2

Also, is that multiplication in-between each term?

Answer 3

sin(20 degrees)*sin(40 degrees)*sin(80 degrees) = 0.2165, or sin(125 degrees)

Answer 4

*sin(12.5 degrees)

Answer 5

sin(20)sin(40) = (1/2)[cos(20) - cos(60)]
=> sin(20)sin(40)sin(80)
= (1/2)[cos(20) - cos(60)]sin(80)
= (1/2)[cos(20)sin(80) - cos(60)sin(80)]
= (1/2)[(1/2)(sin(100)+sin(60)) - (1/2)(sin(140)+sin(20))]
= (1/4)[sin(80) + sin(60) - sin(40) - sin(20)]
= (1/4)sin(60), since sin(80) - sin(40) - sin(20) = sin(60+20) - sin(60-20) - sin(20) = 2cos(60)sin(20) - sin(20) = 0
= (3^1/2)/8