I am given an equation: tan(x) = 5.42

I am supposed to find all of the angles in the interval [0,360] that satisfy the equation above.

So far, I have x = tan^-1(5.42) = 79.6 degrees. Where do I go from here?

OK....you got one angle

Since the tangent is also positive in the 3rd quadrant, add this reference angle to 180° to get the other angle =

259.6°

And that's all of them on [ 0, 360 ] !!!!