Final Answer:
The correct answer is B) Positive co-terminal angles: 0 and 2π, Negative co-terminal angles: π and 3π.
Step-by-step explanation:
The co-terminal angles of a given angle are angles that share the same initial and terminal sides but differ by an integer multiple of 2π. In the case of 5π/2, the positive co-terminal angles can be found by adding multiples of 2π. Adding 2π once results in 9π/2, and adding another 2π leads to 13π/2. These angles represent rotations beyond the original angle while maintaining the same position in the unit circle. On the negative side, subtracting π from 5π/2 gives 3π/2, and subtracting another π results in π/2. These negative co-terminal angles represent rotations in the opposite direction.
Considering the options provided, option B) correctly identifies the nearest two positive co-terminal angles as 0 and 2π, and the nearest two negative co-terminal angles as π and 3π. The calculations align with the principles of co-terminal angles, confirming the correctness of the chosen option. These co-terminal angles are crucial in trigonometry and navigation, providing a comprehensive understanding of angular measurements and aiding in simplifying complex trigonometric expressions and problem-solving.
Therefore, the correct answer is B) Positive co-terminal angles: 0 and 2π, Negative co-terminal angles: π and 3π.