Final answer:
The equation simplifies to cos(x·2π) = -1, which is true at π radians. Therefore, the correct answer is “C. (-1;0)”, representing the cosine of π radians.
Step-by-step explanation:
The question is asking which numbers complete the blanks when solving the equation cosine (x·2π) = −2/2 over the interval [0, 2π]. The equation simplifies to cos(x·2π) = -1, since -2/2 equals -1. In the given interval of the unit circle, the cosine of an angle equals -1 at π radians (180 degrees).
This implies that x·2π must equal π, and solving the equation for x gives us x = π / (2π) = 1/2. Therefore, the correct answer is “C. (-1;0)”, as this represents the cosine of π radians.
The equation (cos(x.2π) = -2/2) is simplified to (cos(x.2π) = -1). In the interval [0, 2π], the cosine of an angle equals -1 at π radians. Thus, (x.2π) must equal π, leading to (x = π/2π =1/2). The correct choice is “C. (-1;0),” representing the cosine of π radians in the given interval. This logical deduction aligns with the characteristics of the unit circle and cosine function.