Question

What angle is coterminal to 51π/2 between 0 and 2π?
a) π/2
b) π
c) 3π/2
d) 2π

Answer 1

The coterminal angle to 51π/2 that lies between 0 and 2π is π/2. This is calculated by subtracting multiples of 2π from 51π/2 until an angle within the 0 to 2π range is reached, which is π/2 in this case.

Step-by-step explanation:

To find an angle coterminal to 51π/2 that lies between 0 and 2π, we need to subtract multiples of 2π (the equivalent of one complete revolution on the unit circle) from 51π/2 until we obtain an angle in the required range. The process is as follows:

1. First calculate the number of complete revolutions: 51π/2 divided by 2π equals 25.5, indicating there are 25 full revolutions plus an extra half revolution.
2. Remove the full revolutions by subtracting 25 * 2π (or 50π) from 51π/2: 51π/2 - 50π/2 = π/2.
3. The remaining angle, π/2, is in the desired range between 0 and 2π.

Therefore, the angle coterminal to 51π/2 between 0 and 2π is π/2. The correct answer to the question is option (a) π/2.