What is the period of the graph of \( y=\sin x \) ? a \( \frac{\pi}{2} \) b \( \frac{\pi}{4} \) c \( \pi \) d \( 2 \pi \)

To determine the period of the function \( y = \sin x \), we can use the definition of the period of a sine function. The period \( T \) of a sine function is the length of one complete cycle of the wave. The general form of the sine function is given by: \[ y = A \sin(Bx + C) + D \] where: - \( A \) is the amplitude, - \( B \) affects the period, - \( C \) is the phase shift, - \( D \) is the vertical shift. The period \( T \) can be calculated using the formula: \[ T = \frac{2\pi}{|B|} \] In the case of \( y = \sin x \), we can see that \( B = 1 \). Therefore, the period is: \[ T = \frac{2\pi}{|1|} = 2\pi \] Thus, the period of the graph of \( y = \sin x \) is \( 2\pi \). The correct answer is: d \( 2 \pi \)