Formula to solve this trigonometry equation?

Question

sin6x + sin2x = 0

Answer 1

Remember that
sin(α) + sin(ß) = 2sin((α+ß)/2)cos((α-ß)/2)
Since the given equation is 0, this means that either
sin((α+ß)/2) = 0 or cos((α-ß)/2) = 0 so that either
(α+ß)/2 = 0 or (α-ß)/2 = π/2. Now 'clean things up' a bit and get
α+ß = 0 and α-ß = π Then substitute back the 6x for α and the 2x for ß to get
8x = 0 => x = 0
and
4x = π => x = π/4
check
sin(0) + sin(0) = 0 Yup.
sin(6*π/4)+sin(2*π/4) = sin(3π/2)+sin(π/2) = -1 +1 = 0
So we're good to go.
And remember that if you add π to those answers, you'll get another set of values that will also work ☺


Doug