9-123. what is the period of y = sin(2πx)? how do you know? homework help

Explanation:

Step1: Recall period - formula for sine function

The general form of a sine function is $y = A\sin(Bx - C)+D$, and its period $T$ is given by the formula $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B

For the function $y = \sin(2\pi x)$, comparing it with $y = A\sin(Bx - C)+D$, we have $A = 1$, $B = 2\pi$, $C = 0$, and $D = 0$.

Step3: Calculate the period

Substitute $B = 2\pi$ into the period - formula $T=\frac{2\pi}{|B|}$. Since $|B|=|2\pi| = 2\pi$, then $T=\frac{2\pi}{2\pi}=1$.

Answer:

1