What is the period of the function sin x?

Correct answer: 2π

The governing concept is the period of a periodic function: the least positive number T such that f(x + T) = f(x) for every x. For the sine function, sin(x + 2π) = sin x, so its fundamental period is 2π radians. This represents one complete revolution on the unit circle, after which the same y-coordinate pattern repeats. Therefore option C is correct. Although 4π also returns the same value, it is not the least positive period. The value π is only half a revolution and gives sin(x + π) = −sin x, so it changes the sign rather than reproducing the function. Similarly, π/2 is a quarter-cycle and cannot reproduce every sine value.