sin(6x)+sin(x)=0

Question

 Needs answers between [0,2pi). solutions in radian answers

Answer 1

We have, sin 6x= -sin x.

 

Thus either 6x = 2kπ - x or 6x = (2k+1)π + x for some integer k.

 

We can set different integers for k in both cases and get all solutions in [0,2π).

 

They are:

 

0

π/5
2π/7
4π/7
3π/5
6π/7
π
8π/7
7π/5
10π/7
12π/7
9π/5