Find the reference angle for the angle $-\frac{25 \pi}{4}$

Step 1 ：Given the angle \(-\frac{25 \pi}{4}\)

Step 2 ：We first find the equivalent positive angle that lies between 0 and \(2\pi\) by adding multiples of \(2\pi\) to the given angle until we get a positive angle in this range.

Step 3 ：The equivalent positive angle is \(\frac{11 \pi}{4}\)

Step 4 ：We then find the reference angle by subtracting the largest multiple of \(\frac{\pi}{2}\) that is less than or equal to the equivalent positive angle.

Step 5 ：The largest multiple of \(\frac{\pi}{2}\) that is less than or equal to \(\frac{11 \pi}{4}\) is \(\frac{10 \pi}{4}\)

Step 6 ：So, the reference angle is \(\frac{11 \pi}{4} - \frac{10 \pi}{4} = \frac{\pi}{4}\)

Step 7 ：Final Answer: \(\boxed{\frac{\pi}{4}}\)