Answer:
[tex]x=14.5\degree[/tex] or [tex]x=165.5\degree[/tex]
Step-by-step explanation:
We want to solve the equation;
[tex]\sin x=\frac{1}{4}[/tex] on the interval [tex][0,360\degree][/tex]
The sine ratio is positive in the first and second quadrant.
We take the sine inverse of both sides of the equation to get;
[tex]x=\sin^{-1}(\frac{1}{4})[/tex]
[tex]x=14.5\degree[/tex]
This is the angle in the first quadrant.
In the second quadrant;
[tex]x=180-14.5[/tex]
[tex]x=165.5\degree[/tex]
