Please help!
"Find all primary solutions in
sin6(theta)+sin3(theta) = 0
$\displaystyle sin(6x) + sin(3x) = 0$
$\displaystyle sin(6x) = - sin(3x)$
$\displaystyle \frac{sin(6x)}{-sin(3x)} = 1$
$\displaystyle -2 cos(3x) = 1$
$\displaystyle cos(3x) = -\frac{1}{2}$
$\displaystyle 3x = arccos(-\frac{1}{2})$
$\displaystyle 3x = \frac{2\pi}{3}$
$\displaystyle x = \frac{2 \pi}{9}$
Now plug x in to the original equation to see if it equals 0
$\displaystyle sin(6(\frac{2\pi}{9}) + sin(3*(\frac{2\pi}{9}) = ?$
$\displaystyle -\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} = 0 $
remember that there are more solutions to this problem such as
$\displaystyle x = \pi,\frac{\pi}{3}, \frac{2 \pi}{3}, \frac{2 \pi}{9},\frac{2 \pi}{9}, \frac{4 \pi}{9}$ and so on