Question

List the solutions between 0, and 2pi for
sin(x/3)= sqrt(2)/2

Answer 1

sin of pi/4 and 3pi/4 is sqrt(2)/2
So it follows that:

Answer 2

\[\frac{x}{3}=\frac{\pi}{4}\]
and
\[x=\frac{3\pi}{4}\]

Answer 3

Also
\[\frac{x}{3}=\frac{3\pi}{4}\]
so
\[x=\frac{9\pi}{4}\]

Answer 4

But 9pi/4 is not between 0 and 2pi so there is only 1 solution.