ANSWER
[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.
EXPLANATION
We want to solve the trigonometric equation;
[tex]Sin(3x)=\frac{1}{4}[/tex]
Since sine ratio is positive, it means the argument,[tex](3x)[/tex] is either the first quadrant or second quadrant.
This implies that;
[tex](3x)=arcsin(\frac{1}{4})[/tex]
[tex](3x)=14.5\degree[/tex] in the first quadrant.
Or
[tex](3x)=180\degree-14.5\degree=165.5\degree[/tex] in the second quadrant.
Since the sine function has a period of [tex]360\degree[/tex], The general solution is given by
[tex](3x)=14.5\degree+360\degree n\:or\:(3x)=165.5\degree +360\degree n[/tex],for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.
Dividing through by 3, we obtain the final solution to be;
[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.
