What is the period of the function y = sin(x)?

The period of the function ( y = \sin(x) ) is ( 2\pi ). This means that the sine function completes one full cycle of its wave pattern as ( x ) increases from 0 to ( 2\pi ). In practical terms, if you were to graph the sine function, you would observe that it starts at 0, rises to a maximum of 1, descends back to 0, continues to a minimum of -1, and finally returns to 0 again at ( 2\pi ). After reaching this point, the behavior of the sine function starts to repeat exactly, implying that the cycle of values for ( y = \sin(x) ) begins anew.

Understanding the concept of periodicity is crucial here, as it applies broadly to trigonometric functions. For sine, every ( 2\pi ) units along the x-axis corresponds to a repetition of the function's pattern. Hence, the fundamental period of the sine function is accurately identified as ( 2\pi ), setting it apart from other potential choices.