Final answer:
To find an angle between 0 and 2π that is coterminal with -π/2, add 2π to get 3π/2 radians. For the angle 12π/11 radians, no alteration is needed as it is already in the desired range.
Step-by-step explanation:
To find an angle between 0 and 2π radians that is coterminal with a given angle, we can add or subtract multiples of 2π (360 degrees) to the given angle until the result falls within the desired range.
Coterminal angles share the same terminal side when drawn in standard position.
Finding a coterminal angle for -π/2 radians
Since -π/2 is less than 0, to find a positive coterminal angle, we will add 2π to -π/2:
-π/2 + 2π = π(1.5) = 3π/2 radians
Finding a coterminal angle for 12π/11 radians
12π/11 is already within 0 and 2π, but if it weren't, we could subtract 2π until we get an angle in the desired range. In this case:
12π/11
This angle is in the required range, so no further computation is necessary.