To find the reference angle, we need to bring each angle to a value within the $0$ to $2\pi$ interval and then determine the angle's position within the unit circle.

(a) $2.5\pi$

1. $2.5\pi$ is already expressed in terms of $\pi$.
2. To find the equivalent angle within $0$ to $2\pi$, subtract $2\pi$: $2.5\pi - 2\pi = 0.5\pi$
3. The angle $0.5\pi$ is in the first quadrant, so the reference angle is simply $0.5\pi$.

Reference angle for $2.5\pi$ is $0.5\pi$.

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(b) $2.5$ (in radians)

1. $2.5$ radians is less than $2\pi$, so we do not need to adjust it.
2. To find the reference angle, we need to determine which quadrant $2.5$ radians is in.
3. $2.5$ radians is between $\pi$ (approximately 3.14) and $0$, meaning it's in the second quadrant.
4. The reference angle is therefore: $\pi - 2.5$
5. Calculating this: $\pi - 2.5 \approx 3.14 - 2.5 = 0.64$

Reference angle for $2.5$ radians is approximately $0.64$ radians.

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(c) $-10\pi$

1. First, we convert $-10\pi$ into a positive angle by adding multiples of $2\pi$ until it is between $0$ and $2\pi$.
2. $-10\pi + 5 \cdot 2\pi = 0$
3. This means that $-10\pi$ is coterminal with $0$.
4. Since it's at the origin, the reference angle is $0$.

Reference angle for $-10\pi$ is $0$.

Would you like more details on these calculations or have any questions?

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Here are five additional questions for further exploration:

1. What is the reference angle for $4.2$ radians?
2. How would you find the reference angle for a negative angle like $-3.5$ radians?
3. Can you determine the reference angle for an angle in degrees, such as $750^\circ$?
4. What is the reference angle for $3\pi/4$?
5. How does the reference angle differ from the actual angle?

Tip: To find the reference angle quickly, remember it is the acute angle between the terminal side of the angle and the x-axis.