To find a positive angle less than 2π that is coterminal with the angle 11π/3, we first need to understand the concept of coterminal angles. Coterminal angles are angles that share the same terminal side when drawn in standard position, which means they differ by a multiple of 2π.
The process for finding a coterminal angle involves subtracting or adding 2π until the angle is within the desired range.
Step 1: Identify the equivalent 2π in terms of the fraction:
- 2π can be written as 6π/3, since 2π = 2 * (3π/3) = 6π/3.
Step 2: Subtract 2π from 11π/3:
11π/3 – 6π/3 = 5π/3.
Step 3: Check if 5π/3 is less than 2π: Yes, since 5π/3 is approximately 5.24, which is less than 6.28.
Therefore, the positive angle less than 2π that is coterminal with 11π/3 is 5π/3.