Final answer:
In the unit circle, an angle terminates on the x-axis if its measure is a multiple of π radians. For the given options, 5/2π radians does not terminate on the x-axis because it equals 450°, which lands the terminal side on the y-axis instead.
Step-by-step explanation:
The student's question is about determining which measure of an angle, represented by theta, does not represent an angle that terminates on the x-axis in the unit circle. An angle that terminates on the x-axis will have an angle measurement that is a multiple of π radians (180°), since a full circle is 2π radians (360°). Let's analyze the options provided:
- A) -5π radians is a valid angle that terminates on the x-axis, as -5π is negative but represents a clockwise rotation that is a multiple of π.
- B) 5/2π radians does not terminate on the x-axis because it equals 2.5π, which is equivalent to a 450° angle, landing the terminal side on the y-axis.
- C) -360° or -1 full revolution, will indeed terminate on the x-axis after completing the circle in a clockwise direction.
- D) 540° represents 1.5 revolutions and the angle will terminate on the x-axis.
- E) π radians or 180° is a half rotation and terminates on the negative x-axis.
Therefore, the angle measurement that does not represent an angle terminating on the x-axis is option B) 5/2π radians.