find both solutions between 0 degrees and 360 degrees of the equation cos = 1/4

Answer 1

I think you mean cos Θ = 1/4

The cosine of an angle is positive in either the 1st or 4th quadrant---i.e. whenever the x component is positive

If the cosine is 1/4, then the angle is arccos (1/4) = 75.52 degrees. The cos of -75.52 degrees is also 1/4