To find a positive angle less than 2π that is coterminal with 11π/3, we first need to understand what coterminal angles are. Coterminal angles are angles that differ by a multiple of 2π. This means that if we add or subtract 2π (or its multiples) from a given angle, we will result in an angle that is coterminal with it.
Given the angle 11π/3, we can start by finding its equivalent angle within the standard range of 0 to 2π. Since 2π can be expressed as a fraction, it is equal to 6π/3. We can find the coterminal angle by subtracting 2π from 11π/3.
So we perform the calculation:
11π/3 – 6π/3 = (11 – 6)π/3 = 5π/3
Now, 5π/3 is less than 2π, and we can verify that it is indeed positive. Therefore, the positive angle less than 2π that is coterminal with 11π/3 is:
5π/3