Final answer:
The reference angle for 127π radians, assuming the correct angle is 12π/7 radians, is π/7 radians (option c). This is found by subtracting the angle from π, the halfway point of a rotation in radians.
Step-by-step explanation:
To find the reference angle of an angle measured in radians, we need to determine the angle's corresponding acute angle within the first quadrant. A full circle is 2π radians (360°). Every angle in the second quadrant will have a reference angle that is the absolute difference between π (half a revolution) and the angle itself.
Let's consider the angle 127π radians. Since the given value is not within the typical range for an angle, it likely contains a typo. If the angle were 127π, it would be many rotations around the unit circle, but that's unrealistic for a typical problem involving reference angles. More likely, the student meant to use a fraction of π, such as 12π/7.
Assuming the angle is 12π/7 radians, which is more than π but less than 2π, the reference angle is:
π - (π - π/7) = π/7.
Therefore, the reference angle is π/7 radians, which corresponds to option (c).