To find the reference angle for \(-515^\circ\), we first need to convert this angle into a standard position angle, which is between \(0^\circ\) and \(360^\circ\).
- Add \(360^\circ\) until the angle is positive: \[ -515^\circ + 360^\circ = -155^\circ \] \[ -155^\circ + 360^\circ = 205^\circ \]
Now, we have \(205^\circ\) in standard position.
- Find the reference angle: The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since \(205^\circ\) lies in the third quadrant, we can find the reference angle using the following formula: \[ \text{Reference angle} = \theta - 180^\circ \] \[ \text{Reference angle} = 205^\circ - 180^\circ = 25^\circ \]
So, the reference angle for \(-515^\circ\) is \(\boxed{25^\circ}\).