If θ = −17π/4, what is the coterminal angle between 0 and 2π?

Correct answer: 7π/4

The governing concept is that coterminal angles differ by an integer multiple of one complete revolution, 2π. We must add a suitable multiple of 2π to −17π/4 until the result lies in the standard interval 0 ≤ θ < 2π. Since 2π = 8π/4, adding 2π once gives −17π/4 + 8π/4 = −9π/4, which is still negative. Adding 2π a second time gives −π/4, still negative. Adding it a third time gives −17π/4 + 24π/4 = 7π/4. This value is positive and less than 2π, so it is the required representative. Therefore option D is correct. The other choices do not result from adding an integer multiple of 2π to the given angle.