# sin(3x) = -1/2

#### TsAmE

Why does sin(3x) = -1/2 equal:

3x = 3.6652 + 2(pi)n nEZ
3x = 5.7596 + 2(pi)n nEZ

and not 3x = pi + pi / 6 + 2(pi)n nEZ
3x = 2pi - pi / 6 + 2(pi)n nEZ

#### Failure

Why does sin(3x) = -1/2 equal:

3x = 3.6652 + 2(pi)n nEZ
3x = 5.7596 + 2(pi)n nEZ

and not 3x = pi + pi / 6 + 2(pi)n nEZ
3x = 2pi - pi / 6 + 2(pi)n nEZ
There is essentially no difference between these two ways of representing the possible values of 3x.

3.6652 is just an approximation for $$\displaystyle \pi+\frac{\pi}{6}$$; and 5.7596 is an approximation for $$\displaystyle 2\pi-\frac{\pi}{6}$$.