Final answer:
None of the provided options (A. π/3, B. 3π/4, C. 5π/4, D. 6/π) match the angles where sin is -1/2 within the 0 to 2π interval; the correct values should be 7π/6 or 11π/6.
Step-by-step explanation:
The question asks for the exact value of sin inverse (-1/2) in the interval between 0 and 2π. To answer this, we must identify at which angles in that interval the sine function takes the value of -1/2. The sine function has a value of -1/2 at 7π/6 and 11π/6 within the specified interval of 0 to 2π. Since these angles are equivalent to 210° and 330° respectively in degrees, and there are no options given in the intervals that match these values, it indicates a typo or mistake in the question as none of the provided options (π/3, 3π/4, 5π/4, 6/π) correspond to the sine of -1/2 within the interval from 0 to 2π.