What is the fundamental period of sin θ?

Correct answer: 2π

The governing concept is the fundamental period: the least positive number T for which f(θ + T) = f(θ) for every θ. For the sine function, one complete revolution on the unit circle has angular measure 2π, and returning to the same point gives sin(θ + 2π) = sin θ. Thus the fundamental period is 2π, so option B is correct. Although 4π also reproduces the sine value, it is not the smallest positive period. A shift of π gives sin(θ + π) = −sin θ, so π is not a period of sine. A shift of π/2 changes the function to cosine in general, so it also cannot be the fundamental period. These distinctions establish both repetition and minimality.