How can I prove that the quotient of two periods of $\sin$ is b?

Question

Let $y(x)=a\sin(bx)+d$ be the function we want to use to describe periodic events. In this context $a > 0$ is supposed to be the amplitude and d the crossing point on the y-axis. Now I read that b is supposed to be $b=\frac{2\pi}{p}$ where p is the period of the process I want to describe. How can I prove that quotient?

Answer 1

$\sin$ has period $2\pi$. So, if $p$ represents 1 period of the event, we have $bp=2\pi$, or $b = \frac{2\pi}{p}$