Final answer:
The two expressions that are opposite to cos(0) are A. cos(π + 0) and D. cos(π - 0), since at an angle of π radians, the cosine function has a value of -1, which is the negative of cos(0).
Step-by-step explanation:
The question asks which two expressions are the opposite of cos(0). To find expressions that are opposite to cos(0), we need to identify the angles for which the cosine function yields a value that is the negative of cos(0) which is 1. The expressions given are cos(π + 0), cos(2π - 0), cos(π/2 - 0), and cos(π - 0).
Looking at the unit circle, the cosine function is equal to -1 at an angle of π radians. Therefore, cos(π + 0) and cos(π - 0) will both yield -1, making them the opposite of cos(0). On the other hand, cos(2π - 0) is the same as cos(0), since the cosine function is periodic with a period of 2π. Expression cos(π/2 - 0) results in 0, as cos(π/2) is 0. Thus, the two expressions that are opposite of cos(0) are option A (cos(π + 0)) and option D (cos(π - 0)).