Question

How do you expand sin(2x) to sin(8x)?

Answer 1

So we're starting with sin(2x) and we want to write the expression in terms of sin(8x)?

Answer 2

Or the other way around..? :o

Answer 3

sin(8x) = 2sin(4x)cos(4x) = 4sin(2x)cos(2x)cos(4x) by applying the double angle formula twice. Check out this link: http://www.sosmath.com/trig/douangl/douangl.html

Answer 4

I first tried applying the half angle formula with 2x, but that's a nightmare, and doesn't appear to lead anywhere fruitful.