(a) Find an angle $\theta$, with $0^{\circ}<\theta<360^{\circ}$, that has the same cosine as $65^{\circ}$ (but is not $65^{\circ}$ ). (b) Find an angle $\theta$, with $0^{\circ}<\theta<360^{\circ}$, that has the same sine as $65^{\circ}$ (but is not $65^{\circ}$ ).

Step 1 ：For part (a), we know that cosine is positive in both the first and fourth quadrants. So, the angle that has the same cosine as \(65^{\circ}\) would be in the fourth quadrant and can be found by subtracting \(65^{\circ}\) from \(360^{\circ}\).

Step 2 ：For part (b), sine is positive in the first and second quadrants. So, the angle that has the same sine as \(65^{\circ}\) would be in the second quadrant and can be found by subtracting \(65^{\circ}\) from \(180^{\circ}\).

Step 3 ：The angle that has the same cosine as \(65^{\circ}\) is \(\boxed{295^{\circ}}\) and the angle that has the same sine as \(65^{\circ}\) is \(\boxed{115^{\circ}}\).