Chapter 5, Problem 11PTB

Find all solutions of each equation.

$\sin \frac{x}{3}=\frac{\sqrt{2}}{2}$

a. $x=\frac{\pi }{4}+2\pi n$ and $x=\frac{3\pi }{4}+2\pi n$, for any integer n

b. $x=\frac{\pi }{4}+6\pi n$ and $x=\frac{\pi }{12}+6n\pi$, for any integer n

c. $x=\frac{3\pi }{4}+6\pi n$ and $x=\frac{9\pi }{4}+6\pi n$, for any integer n

d. $x=\frac{3\pi }{4}+2\pi n$ and $x=\frac{5\pi }{4}+2\pi n$, for any integer n