The period of the sine function y = sin(bx) is determined by the coefficient ‘b’. The general formula for the period of the sine function is given by:
Period = rac{2C0}{|b|}
This means that the period of the sine function is the length of one complete cycle of the wave. When you change the value of ‘b’, you change how quickly the sine function oscillates.
For example, if b = 1, the period is 2π (which corresponds to the standard sine wave). If b = 2, the period becomes π, meaning the wave completes its cycle twice as fast.
Hence, for any value of ‘b’ other than zero, the sine function will repeat its values every rac{2C0}{|b|} units along the x-axis. However, if b = 0, the sine function becomes constant (y = 0), and thus does not have a defined period in the traditional sense.