Final answer:
The angle between 0 and 2π equivalent to 13π/4 is found by subtracting multiples of 2π and is 5π/4, corresponding to answer choice (c). Therefore, the angle between 0 and 2π that is equivalent to 13π/4 is 5π/4, which corresponds to answer choice (c).
Step-by-step explanation:
To find the angle between 0 and 2π that is equivalent to 13π/4, we first note that 13π/4 is larger than 2π. To find an equivalent angle within the range of 0 to 2π, we can subtract multiples of 2π until we are within this range.
To find the angle between 0 and 2π that is equivalent to 13π/4, we can use the fact that one full revolution around a circle is equal to 2π radians.
We can rewrite 13π/4 as a mixed number by dividing 13 by 4, which gives us 3 remainder 1. So, 13π/4 is equivalent to (3π+π/4). Since 3π is equal to 6π/2 or 2π, the angle is equal to 2π+π/4. Simplifying, we get 9π/4. But since the angle needs to be between 0 and 2π, we subtract 2π to get 9π/4 - 2π = 9π/4 - 8π/4 = π/4.
Since 13π/4 is the same as 3π/4 plus three full rotations (3×2π), the equivalent angle within one rotation can be found by subtracting these full rotations:
13π/4 - 3×2π = 13π/4 - 24π/4 = -11π/4
However, since we want a positive angle, we add 2π (which is the same as adding 8π/4) back to our answer:
-11π/4 + 8π/4 = -3π/4
To get to the positive equivalent, we add another 2π:
-3π/4 + 8π/4 = 5π/4
Therefore, the angle between 0 and 2π that is equivalent to 13π/4 is 5π/4, which corresponds to answer choice (c).