Final answer:
The angle \(\phi\) between \(0^\circ\) and \(360^\circ\) with the same cosine as \(57^\circ\) is \(303^\circ\), due to the symmetry of the cosine function in the unit circle.
Step-by-step explanation:
To find another angle \(\phi\) between \(0^\circ\) and \(360^\circ\) that has the same cosine as \(57^\circ\), we should remember that the cosine function is positive in both the first and fourth quadrants and has the property \(\cos(\theta) = \cos(360^\circ - \theta)\).
Therefore, the angle with the same cosine as \(57^\circ\) but lies in the fourth quadrant is \(360^\circ - 57^\circ = 303^\circ\).
This is because the cosine function is even, meaning \(\cos(\theta) = \cos(-\theta)\), which allows us to utilize the symmetry of the unit circle. Hence, the angle \(\phi\) which has the same cosine as \(57^\circ\) is \(\strong{303^\circ}\).