Final answer:
An angle between 0 and 2π that is coterminal with 18π/5 can be found by subtracting multiples of 2π until we get an angle within that range.
Step-by-step explanation:
An angle that is coterminal with 18π/5 can be found by adding or subtracting any multiple of 2π to the given angle. In this case, one full revolution is equal to 2π. So, to find an angle between 0 and 2π that is coterminal with 18π/5, we need to subtract or add multiples of 2π from 18π/5 until we get an angle within that range.
To simplify 18π/5, we can divide the numerator and the denominator by the greatest common divisor, which is π. This gives us 18/5.
Using this simplified fraction, we can find an angle that is coterminal with 18π/5 by multiplying 18/5 by 2π:
18/5 * 2π = 36π/5
Since 36π/5 is greater than 2π, we need to subtract multiples of 2π until we get an angle between 0 and 2π. Starting with 36π/5, we subtract 2π:
36π/5 - 2π = 26π/5
Now we have an angle between 0 and 2π (26π/5) that is coterminal with 18π/5.