Final answer:
To find the angle between 0 and 2π coterminal with 51π / 2, subtract multiples of 2π until within that range. The coterminal angle is π / 2.
Step-by-step explanation:
The question asks us to find an angle between 0 and 2π that is coterminal with 51π / 2. To find a coterminal angle within one full rotation (0 to 2π), we can subtract multiples of 2π from the given angle until we get into that range. Starting with 51π / 2, we can see that:
51π / 2 = 25π + π / 2
Since 25π represents 12 full rotations (because 25 = 2 × 12 + 1), we can subtract this from 51π / 2 to get the remaining part, which is π / 2. Therefore, the coterminal angle between 0 and 2π that corresponds with 51π / 2 is π / 2.